Question: When is China founded?

History of China

He met with U.S. President Richard Nixon and Secretary of State Henry Kissinger and, as a skilled diplomat, succeeded in establishing great power relations with the United States.


Question: When is China founded?

History of China

It is largely thanks to Mr Zhou that the People's Republic of China received a seat previously belonging to Taiwan at the UN in 1971.


Question: When is China founded?

History of China

[252] [253] Mao, however, was not willing to name Zhou as his own successor, as Zhou fell into Mao's disfavor in his final years.


Question: When is China founded?

History of China

This would not even have been possible, as both Mao and Zhou began to be sickly.


Question: When is China founded?

History of China

Zhou Enlai died in January 1976.


Question: When is China founded?

History of China

The popular prime minister was genuinely mourned and millions of Peking people watched his funeral.


Question: When is China founded?

History of China

Officially, Zhou's mourning was curtailed and leftists in the party accused him of being a capitalist.


Question: When is China founded?

History of China

After Zhou's death, unrest first arose in his hometown of Nanjing, from where they also spread to Beijing.


Question: When is China founded?

History of China

In Beijing, the situation escalated in April 1976 into the Tiananmen Square incident, where a gang of mourners from Zhou was dispersed by violence.


Question: When is China founded?

History of China

The Communist Party blamed Deng Xiaoping, who was considered to be the same path traveller as the late Zhou Enlai, as the initiator of the incident.


Question: When is China founded?

History of China

Mao was no longer in the months following the Tiananmen incident at the head of the country due to his health.


Question: When is China founded?

History of China

Mao Zedong died in September 1976.


Question: When is China founded?

History of China

[254] After Mao's death, the members of the four coples were imprisoned and Hua Guofeng, who was the successor appointed by Mao, rose to the leadership of the country.


Question: When is China founded?

History of China

[255] After Mao, a few years of power struggle between conservative and reformist politicians followed.


Question: When is China founded?

History of China

[238] The reformist Deng Xiaoping, who had fallen into Mao's unpopularity during the Cultural Revolution, soon emerged as the most influential politician.


Question: When is China founded?

History of China

[238] [255] Deng, however, was under Zhou Enlai's protection and may well have thanked him for preserving his life.


Question: When is China founded?

History of China

[252] Deng emerged in the late 1970s as the most prominent politician in the reformist wing of the party.


Question: When is China founded?

History of China

The reforms he pushed, such as economic modernization and opening up to the outside world, started a period of reform in China.


Question: When is China founded?

History of China

[238] [249] Proponents of modernisation led by Deng gained increasing influence within the party and Deng was thus able to win over the party's more conservative politicians.


Question: When is China founded?

History of China

[249] [255] [256] The political views of Hua Guofeng and Deng, who emerged as figurehead of the party, diverged and in 1981, Hua was forced to resign his post.


Question: When is China founded?

History of China

[255] [257] [258] He was succeeded at the head of the party by Deng's protégé Hu Yaobang.


Question: When is China founded?

History of China

Deng himself again continued as chairman of China's Central Military Commission.


Question: When is China founded?

History of China

[255] The first major reforms of Deng Xiaoping's reign were the dismantling of collectivization of agriculture and a return to private agriculture.


Question: When is China founded?

History of China

[256] [249] Private enterprise was also limited in the industrial and services sector and the restructuring of state enterprises in order to give greater influence to market forces.


Question: When is China founded?

History of China

[249] Special Economic Zones began to be established in the country in coastal areas in order to better open the market to foreign trade.


Question: When is China founded?

History of China

[256] The first Special Economic Area was Shenzhen, bordering Hong Kong, which quickly grew from a small peasant village into a major trading and industrial city.


Question: When is China founded?

History of China

[249] Despite economic development, Chinese policy did not significantly change.


Question: When is China founded?

History of China

[249] Economic reforms did not please the old wing of the Communist Party either.


Question: When is China founded?

History of China

[256] [259] The old wing of the party was also dissatisfied with Hu Yaobang's habit of allowing the country's critical intelligentsia to operate free.


Question: When is China founded?

History of China

[259] Hu also had an interference with Deng Xiaoping, for he was too liberal even for Deng's mind.


Question: When is China founded?

History of China

[259] [248] In late 1986, extensive intellectuals and student demonstrations broke out, which spread across the country.


Question: When is China founded?

History of China

Protesters called for regime reform and Western-style democracy.


Question: When is China founded?

History of China

The situation led to Hu's dismissal in 1987 and Zhao Ziyang was named as his successor.


Question: When is China founded?

History of China

[259] [256] The threat of harder grips caused protests to subside, [259] but this changed when Hu Yaobang died in the spring of 1989.


Question: When is China founded?

History of China

[256] Hu was very popular among the students and these organized mass rallies in his memory.


Question: When is China founded?

History of China

These evolved into demonstrations that filled Celestial Peace Square in May 1989.


Question: When is China founded?

History of China

[249] Zhao Ziyang tried unsuccessfully to find a peaceful solution to the protracted demonstration.


Question: When is China founded?

History of China

For Deng, Zhao's conciliatory actions did not take place and the situation led to Zhao's removal from office.


Question: When is China founded?

History of China

[260] Deng Xiaoping took command back into his own hands and ordered the army to stop the demonstrations by force.


Question: When is China founded?

History of China

On 4 June, the army violently dispersed the demonstration, causing hundreds of casualties.


Question: When is China founded?

History of China

The carnage caused a three-year suspension of economic reforms and deterioration of relations with Western countries.


Question: When is China founded?

History of China

[256] Economic reforms continued under the leadership of Jiang Zemin, who was appointed Secretary-General.


Question: When is China founded?

History of China

In China, the command economy was abandoned in 1993 and talk of a socialist market economy began.


Question: When is China founded?

History of China

In practice, this meant that the Communist Party renounced Marxism.


Question: When is China founded?

History of China

[256] [261] In Deng Xiaoping's final years, China began to prepare for the time after him and Jiang built himself a leader cult larger than Deng.


Question: When is China founded?

History of China

He therefore faced a third Taiwan Strait crisis in the mid-1990s when relations with Taiwan became strained again, under which he sought to show nationalist leadership.


Question: When is China founded?

History of China

[262] Deng Xiaoping died at the age of 93 in February 1997.


Question: When is China founded?

History of China

In July of the same year, Britain returned Hong Kong's leased territory to China, a major prestige gain for Jiang Zemin.


Question: When is China founded?

History of China

As a result of the UK-China negotiations, Hong Kong will retain its internal autonomy for another 50 years after reunification and Hong Kong will be subject to the so-called One Country, Two Systems principle.


Question: When is China founded?

History of China

[263] The most significant reforms of Jiang's rule period were the economic reforms of the late 1990s, when state enterprises were reorganized and the country took a major step towards a market economy.


Question: When is China founded?

History of China

As a result, China, thanks to economic growth, rose to the ranks of the world's economic superpowers.


Question: When is China founded?

History of China

As a counterbalance to these, many societal problems and environmental disasters were exacerbated.


Question: When is China founded?

History of China

[264] China became a member of the World Trade Organization in 2001, integrating it more firmly into world trade.


Question: When is China founded?

History of China

[265] In the first decade of the 21st century, the country's economy grew at a pace and by the time of entering the 2010s it was already the second largest national economy in the world.


Question: When is China founded?

History of China

The country is also urbanized at a pace, in 2015 was the first time the situation that the majority of Chinese people lived in cities.


Question: When is China founded?

History of China

[256] Sources Citation error, replace with {{cite book| author = Haw, Stephen G.| title = Travel Guide to History - China| others = Translated by Top, Anne| location = English | publisher = Oy UniPress AB| year = 2005| id = ISBN 951-519-110-3}} Citation error, replace with {{cite book| author = Malmqvist, Göran| title = The Great World History of Otava 5 - Great Powers of the Easter| location = Keuruu| publisher = Publishing Company Otava| year = 1983| id = ISBN 951-51-07161-0}} Citation error, replace with {{cite book| author = Malmqvist, Göran| title = Great World History of Otava 12 - Age of Enlightenment| location = Keuruu| publisher = Publishing company Otava| year = 1985| id = ISBN 951-1-08415-1}} Citation error, replace with {{cite book| author = Malmqvist, Göran| title = The Great World History of Otava 15 - Age of Imperialism| location = Keuruu| publisher = Publishing Company Otava| year = 1986| id = ISBN 951-1-09016-X}} Citation error, replace with {{cite book| author = Bjøl, Erling| title = Otava Great World History 19 - New World Order| location = Keuruu| publisher = Publishing Company Otava| year = 1987| id = ISBN 951-1-09631-1}} error, replace with {{cite book| author = Huotari, Tauno-Olavi & Seppälä, Pertti| title = Chinese culture| publisher = Otava| year = 2005 (5th edition) | id = ISBN 951-1-15943-7}} Citation error, replace with {{cite book| author = Shaugnessy, Edward L.| title = Fascinating China| publisher = Gummerus| year = 2006| id = ISBN 951-20-7160-6}} Citation error, replace with {{cite book| author = Scarpari Maurizio| title = Historical cultures - China| others = Translated by Salminen, Raimo| publisher = Weilin+Göös Oy| year = 2008| id = ISBN 978-951-0-32992-4}} Citation error, replace with {{cite book| author = Paltemaa, Lauri| title = Brief Introduction to Chinese History| publisher = University of Turku East Asian Studies and Education Center| year = 2018| id = ISBN 978-951-29-7157-2| format = [online version]}} Citation error, replace with {{cite book| author = Paltemaa, Lauri; Vuori, Juha A.| title = History of the People's Republic of China| publisher = Gaudeamus Oy| year = 2012| id = ISBN 978-952-495-258-3}} References on the topic elsewhere * Category:Key articles on screening


Question: When is Korpilahti founded?

Korpilahti

Korpilahti (informally) is a former municipality of Finland located in central Finland, between Muurame and Jämsä, on both sides of Päijänne.


Question: When is Korpilahti founded?

Korpilahti

The municipality joined the city of Jyväskylä in early 2009.


Question: When is Korpilahti founded?

Korpilahti

The neighbouring municipalities of Korpilahti were Joutsa, Jyväskylä mlk, Jämsä, Jämsänkoski, Luhanka, Muurame, Petäjävesi and Toivakka.


Question: When is Korpilahti founded?

Korpilahti

The municipality of Korpilahti had a population in 2009 [1] and about 4500 cottagers in addition to these during the summer period.


Question: When is Korpilahti founded?

Korpilahti

The municipality covered an area of km2, of which km² were bodies of water.


Question: When is Korpilahti founded?

Korpilahti

[2] It contains land on both sides of Päijänne, and there are about 200 lakes in the area.


Question: When is Korpilahti founded?

Korpilahti

The population is almost entirely Finnish-speaking.


Question: When is Korpilahti founded?

Korpilahti

In the sub-division of Jyväskylä, Korpilahti forms the Korpilahti Sub-Region.


Question: When is Korpilahti founded?

Korpilahti

In 2009, the Korpilahti Sub-Region had 5,071 inhabitants and in 2016 it had a population of 4,960 [3].


Question: When is Korpilahti founded?

Korpilahti

Traffic through Korpilahti passes through Highway 9, formerly also Highway 4.


Question: When is Korpilahti founded?

Korpilahti

In the former Korpilahti district, on the Korpilahden-Luhanga highway (No.610), the Kärkistensalmi Bridge, built between 1995 and 1997 and replaced the loss, is located.


Question: When is Korpilahti founded?

Korpilahti

Sub-regional road 610, the only road connection connecting the western and eastern parts of Korpilahti, continues through Luhanga to Joutsa, where it joins Highway 4 (formerly Base Road 59) east of Päijänne.


Question: When is Korpilahti founded?

Korpilahti

At the end of the 1970s, a short track from Jämsänkoski to Jyväskylä was completed through Korpilahti, and greatly shortened the train journey from Tampere to Central Finland.


Question: When is Korpilahti founded?

Korpilahti

The railway section has the longest railway tunnel in Finland in the Korpilahti region, the Lahtenvuori Tunnel, approximately 4.2 kilometres long.


Question: When is Korpilahti founded?

Korpilahti

The railway is irrelevant for local transport conditions as it has no passenger transport facilities in the Korpilahti district.


Question: When is Korpilahti founded?

Korpilahti

Korpilahti belongs to the catchment area of both Jyväskylä and Jämsä; the centre of each is about 30 km from the Korpilahti church village.


Question: When is Korpilahti founded?

Korpilahti

[4] Distances from Korpilahti Helsinki 240 km Jyväskylä 30 km Lahti 145 km Tampere 120 km History Prehistoric artifacts found in the Korpilahti area show that people have moved around the region at least 5000, perhaps as early as 7000 years ago.


Question: When is Korpilahti founded?

Korpilahti

Hämäish lot visitors appeared in the Korpilahti area around the 400—5th centuries after the beginning of the period, as is inferred from the oval fire stones found.


Question: When is Korpilahti founded?

Korpilahti

However, a solid settlement did not form until much later, and the area remained the hinterland of Jämsä for a long time.


Question: When is Korpilahti founded?

Korpilahti

The eastern part of Korpilahti in Päijänne was a wilderness area for the keepers of Askkala and Sääksmäki.


Question: When is Korpilahti founded?

Korpilahti

Disputes arising from wilderness holdings were also resolved by the district authorities, and the Jämsä district protocols for 1492 and 1495 mentioned names such as Korospohja, Särkäntaipale and Kiikäsvaha.


Question: When is Korpilahti founded?

Korpilahti

According to the Land Book of 1539 there were 13 houses in the area of present-day Korpilahti.


Question: When is Korpilahti founded?

Korpilahti

[4] Korpilahti was formed as Jämsä Chapel in 1691 and included the later Muurame and Säynätsalo.


Question: When is Korpilahti founded?

Korpilahti

The first church of the keeper was damaged during the Great Wrath and a new church was completed in 1755 under the leadership of Arvi Junkkarinen, a Leppävirtan.


Question: When is Korpilahti founded?

Korpilahti

The present church was built according to drawings by architect Charles Bass between 1823 and 1826.


Question: When is Korpilahti founded?

Korpilahti

Korpilahti was ordered by an imperial letter of order in October 1861 to be separated into an independent parish, but the first vicar of its own was not obtained until 1872.


Question: When is Korpilahti founded?

Korpilahti

Korpilahti had a maximum population of over 10,000 people in the late 19th and early 20th centuries.


Question: When is Korpilahti founded?

Korpilahti

Muurame separated from Korpilahti in 1920 — the population of Korpilahti declined by almost 3000 people — and Sääynätsalo further from Muurame in 1923.


Question: When is Korpilahti founded?

Korpilahti

[4] Korpilahti was inhabited after the Continuation War by settlers from Valkjärvi.


Question: When is Korpilahti founded?

Korpilahti

[5] Korpilahti remained a traditional farming and forestry manager until the 1950s, when small-scale industries began to emerge in the locality.


Question: When is Korpilahti founded?

Korpilahti

Until 1960, Korpilahti belonged to Häme County, from where it was transferred to the newly created Central Finland County.


Question: When is Korpilahti founded?

Korpilahti

During the 1960s, Korpilahti's population began to decline sharply, even more than in many more remote municipalities.


Question: When is Korpilahti founded?

Korpilahti

Exclusively during 1965, the population decreased by 197 people.


Question: When is Korpilahti founded?

Korpilahti

Nearby Jyväskylä attracted especially young migrants.


Question: When is Korpilahti founded?

Korpilahti

[4] Population The following graph shows the population trend of Korpilahti every ten years between 1880 and 1970 with an additional 1975 population.


Question: When is Korpilahti founded?

Korpilahti

In 1920, Muurame was separated from Korpilahti, which had 2,763 inhabitants at the time.


Question: When is Korpilahti founded?

Korpilahti

The Muurami was further separated in 1923 into the parish of Säynätsalo by an area with a population of 581 people.


Question: When is Korpilahti founded?

Korpilahti

[6] Villages Korpilahti villages include e.g.


Question: When is Korpilahti founded?

Korpilahti

Moksi, Tikkala, Oittila, Saukkola, Ylä-Muuratjärvi, Putkilahti, Saakoski and Sarvenperä.


Question: When is Korpilahti founded?

Korpilahti

Attractions Along Seututie 610, just under ten kilometres from Kärkistensalmi towards Luhanga, is currently a nature reserve, which rises more than 120 metres above the surface of Päijänne, whose plant variety is exceptionally abundant compared to the environment.


Question: When is Korpilahti founded?

Korpilahti

The mountain had one of the steepest climbs of Finnish national roads until the current road was completed on the eastern side of the earlier road in 1984.


Question: When is Korpilahti founded?

Korpilahti

Imatran Voima was planning a pumped power station on the mountain since the 1960s, which was intended to be the first of its kind in Finland, but this project was finally buried in the early 2000s.


Question: When is Korpilahti founded?

Korpilahti

One of the protected measuring points of the UNESCO World Heritage listed Struve chain is located on the former Korpilahti, Oravi Mountain.


Question: When is Korpilahti founded?

Korpilahti

A consultative referendum on joining Jyväskylä was held in Korpilahti.


Question: When is Korpilahti founded?

Korpilahti

There were 2,505 people who voted, of whom 1,303 (52.0%) opposed the union and 1,055 (42.1%) were in favour.


Question: When is Korpilahti founded?

Korpilahti

Despite the outcome of the vote and the civic debate, Korpilahti Municipal Council decided by a vote of 17-10 that the municipality would merge with Jyväskylä on 1 January 2009.


Question: When is Korpilahti founded?

Korpilahti

Jyväskylä also approved the joint.


Question: When is Korpilahti founded?

Korpilahti

In addition, according to the decision of 18 February 2008, the new city was joined by the rural municipality of Jyväskylä.


Question: When is Korpilahti founded?

Korpilahti

An amendment to the division of municipalities was submitted to the Ministry of the Interior to annex the southern part of Korpilahti to Jämsa.


Question: When is Korpilahti founded?

Korpilahti

The area proposed for annexation accounted for 20.8% of the municipal area and 12.9% of the municipal population lived in the area.


Question: When is Korpilahti founded?

Korpilahti

Twenty-two comments arrived in the municipality by the deadline, 6 in favour and 16 opposing the proposed annexation to Jämsä.


Question: When is Korpilahti founded?

Korpilahti

Anssi Nykänen, the former mayor of Korpilahti, and Markku Andersson, the mayor of Jyväskylä, supported the union with Jyväskylä.


Question: When is Korpilahti founded?

Korpilahti

Instead, Jyväskylä MPs and city councillors Petri Neittaanmäki and Ahti Vielma opposed the union.


Question: When is Korpilahti founded?

Korpilahti

Food culture Korpilahti's keeper dishes were named in the 1980s as blood palttu and lingonberries and rattamate, or berry warmth.


Question: When is Korpilahti founded?

Korpilahti

[7] Sources on the topic elsewhere * Category:Key articles on screening


Question: When was the concept of history invented?

History of mathematics

The history of mathematics is very long.


Question: When was the concept of history invented?

History of mathematics

Mathematics, along with physics and astronomy, is one of the oldest disciplines.


Question: When was the concept of history invented?

History of mathematics

The Genesis of Mathematics Accurately elucidating the first steps of mathematics is impossible, as mankind learned to calculate before the art of writing was born.


Question: When was the concept of history invented?

History of mathematics

Thus, no written documentation of the first rules of calculation or geometric outlines remain.


Question: When was the concept of history invented?

History of mathematics

The early history of mathematics can best be studied through archaeological discoveries, linguistics, and animal observation.


Question: When was the concept of history invented?

History of mathematics

It has been found that many animals are capable of distinguishing the size difference between troops smaller than at least five embryos.


Question: When was the concept of history invented?

History of mathematics

Thus, one can assume that some concept of a figure is very old.


Question: When was the concept of history invented?

History of mathematics

This is also supported by the breakdown of the grammatical number of many languages into one and many, in some cases two and three.


Question: When was the concept of history invented?

History of mathematics

From understanding the difference between two stones and three stones, it has probably gone a long way to realising the abstract concept of 'three' as linking together three stones and three trees.


Question: When was the concept of history invented?

History of mathematics

[1] This idea is supported by the fact that many animals that perceive troop size differences are unable to do this.


Question: When was the concept of history invented?

History of mathematics

Furthermore, the first reading words to appear in languages have originally meant, for example, two stones.


Question: When was the concept of history invented?

History of mathematics

The figure has thus been difficult to perceive as a disconnected concept from its connection.


Question: When was the concept of history invented?

History of mathematics

According to some theories, ordinal numbers would have arisen before cardinal numbers.


Question: When was the concept of history invented?

History of mathematics

This has been justified by the fact that in many rituals and myths, the order of events and persons has played an important part.


Question: When was the concept of history invented?

History of mathematics

[1] However, languages do not support this notion, as in almost all languages an ordinal number is formed by inflecting a cardinal number.


Question: When was the concept of history invented?

History of mathematics

The oldest archaeological evidence for counting numbers is about 30,000 years old.


Question: When was the concept of history invented?

History of mathematics

The bone found in the Czech Republic has a total of 55 notches broken down into groups of five.


Question: When was the concept of history invented?

History of mathematics

Five has been a natural choice as a suitable number because there are five fingers on one hand.


Question: When was the concept of history invented?

History of mathematics

Ten (fingers of two hands) and twenty (fingers and toes) have also been early stock figures for reading systems.


Question: When was the concept of history invented?

History of mathematics

In a survey of American Indian tribes, one-third used the five-system, a third used the ten-system, just under a third the binary system, and the rest the tri-system.


Question: When was the concept of history invented?

History of mathematics

There is evidence of the twenty-system mostly from Europe, where its remnants can still be seen in languages, French 80 (quatre-vingt) is four to twenty in Finnish.


Question: When was the concept of history invented?

History of mathematics

The earliest written evidence seems to have favoured the five-system, but as the language gained a distinct formal form, the ten-system has emerged as the most common.


Question: When was the concept of history invented?

History of mathematics

[1] The early stages of geometry are even harder to ascertain.


Question: When was the concept of history invented?

History of mathematics

The Greeks placed the genesis of geometry in ancient Egypt, where it was needed for surveying.


Question: When was the concept of history invented?

History of mathematics

However, it is clear that advanced geometric thinking was not born out of thin air at the time; there has already been some kind of geometric figuring ability in the past.


Question: When was the concept of history invented?

History of mathematics

Many other animals, especially monkeys, are able to perceive form as an abstract thing detached from a particular object, and group different objects based on shape into groups.


Question: When was the concept of history invented?

History of mathematics

The oldest evidence of creative geometric thinking can be seen in cave paintings showing geometric patterns and various braiding works.


Question: When was the concept of history invented?

History of mathematics

Already in them you can see, for example, the idea of uniformity and symmetry of patterns.


Question: When was the concept of history invented?

History of mathematics

[2] One of the oldest such works is a cave found in South Africa with geometric patterns scrawled on its walls estimated as early as 70000 years ago.


Question: When was the concept of history invented?

History of mathematics

[3] Ancient Egyptian mathematics (3000—500 BCE)


Question: When was the concept of history invented?

History of mathematics

Along with the Sumerians, Egyptians are the first people to learn the art of writing.


Question: When was the concept of history invented?

History of mathematics

The earliest documents on Egyptian pictorial writing, hieroglyphs, are over 5500 years old, and the first surviving number markings are over 5000 years old.


Question: When was the concept of history invented?

History of mathematics

The Egyptians used the ten-system, and their way of denoting numbers was of the same type as that of the Romans.


Question: When was the concept of history invented?

History of mathematics

Ten for potencies up to at least one million was each its own mark, and the number of these characters expressed that number of ten potencies in the chapter.


Question: When was the concept of history invented?

History of mathematics

For example, 1362749 was marked Later, a shortening notation was introduced, where, for example, a quad had its own mark, a horizontal line.


Question: When was the concept of history invented?

History of mathematics

[4] The main sources for the level of ancient Egyptian mathematics are certain preserved papyri containing instructions and tasks.


Question: When was the concept of history invented?

History of mathematics

The most extensive of these dates to about 1650 BCE.


Question: When was the concept of history invented?

History of mathematics

the Ahmes papyrus [5], another significant source dates from about 1890 BCE.


Question: When was the concept of history invented?

History of mathematics

Moscow papyrus.


Question: When was the concept of history invented?

History of mathematics

Based on these, it has been found that Egyptians knew how to use fractions.


Question: When was the concept of history invented?

History of mathematics

However, they stuck to unit fractions (of the form 1/n) and number 2/3.


Question: When was the concept of history invented?

History of mathematics

Other fractions they considered to be intolerable.


Question: When was the concept of history invented?

History of mathematics

The Ahmes papyrus shows figures of the form 2/n as the sum of unit fractions with values of n 5 to 101.


Question: When was the concept of history invented?

History of mathematics

The Egyptians did not actually use multiplication or division; instead, they performed these operations by duplicating or halving the numbers and adding them together.


Question: When was the concept of history invented?

History of mathematics

Multiplication by ten was also used.


Question: When was the concept of history invented?

History of mathematics

The author of Ahmes's papyrus has also been able to divide figures in any respect, which one might imagine was important for state taxation and wages.


Question: When was the concept of history invented?

History of mathematics

[4] In addition to arithmetics, Egyptians have been proficient in the rudiments of algebra and geometry.


Question: When was the concept of history invented?

History of mathematics

The Ahmes papyrus shows a method for solving first-order equations of simple form.


Question: When was the concept of history invented?

History of mathematics

In addition, it appears the first known mathematical proof in which it is proved by calculating a given number to implement an equation.


Question: When was the concept of history invented?

History of mathematics

In geometry, Egyptians have been able to calculate the fields of isosceles and rectangular triangles, as well as directional ones, by breaking them up into appropriate triangles and assembling a rectangle of triangles.


Question: When was the concept of history invented?

History of mathematics

Using the same method three-dimensionally, they knew how to calculate the volume of the truncated pyramid.


Question: When was the concept of history invented?

History of mathematics

Contrary to what is often mentioned, there is no indication of the use of the Pythagorean theorem in preserved sources.


Question: When was the concept of history invented?

History of mathematics

Of the trigonometric relations, Egyptian mathematicians had in place the ratio equivalent to the current cotangent required for the construction of the pyramid.


Question: When was the concept of history invented?

History of mathematics

[4] The mathematics of the Egyptians seems to have developed early to a level that has allowed the construction of pyramids, the measurement of plots, and the functioning of an advanced economy.


Question: When was the concept of history invented?

History of mathematics

However, after the Ahmes papyrus, its development seems to have stalled.


Question: When was the concept of history invented?

History of mathematics

Apparently mathematics was only developed for practical needs.


Question: When was the concept of history invented?

History of mathematics

Among the greatest weaknesses in Egyptians' mathematics was perhaps approximation due to practicality.


Question: When was the concept of history invented?

History of mathematics

The value of silicon used by the Egyptians was 3+13/81, which in itself is not a bad approximation.


Question: When was the concept of history invented?

History of mathematics

However, they seem to have assumed it was accurate because they knew it was almost correct.


Question: When was the concept of history invented?

History of mathematics

Similarly, the Egyptians calculated the area of a quadrilateral to be the input of the mean of opposite sides, giving precise approximations to the quadrilateral close to the square.


Question: When was the concept of history invented?

History of mathematics

The formula for the triangle field is also derived from this, according to which the area is the mean of the two sides multiplied by the half of the third.


Question: When was the concept of history invented?

History of mathematics

This indicates that the Egyptians knew how to derive another formula from the formula and even used zero as the length of one page.


Question: When was the concept of history invented?

History of mathematics

However, the formula is wrong due to the original approximation assumption.


Question: When was the concept of history invented?

History of mathematics

[4] [6] Mathematics in Mesopotamia (3000—500 BC)


Question: When was the concept of history invented?

History of mathematics

The mathematics developed in the Mesopotamian region has tended to be called Babylonian, although other peoples lived in the area besides the Babylonians.


Question: When was the concept of history invented?

History of mathematics

The reason for this is the fairly unified culture of the region.


Question: When was the concept of history invented?

History of mathematics

Much more evidence of Babylonian mathematics has survived than Egyptian mathematics, as peoples in the region used clay tables better preserved from papyrus as their writing platform.


Question: When was the concept of history invented?

History of mathematics

The first significant people of the region, the Sumerians, learned the art of writing more than 5,000 years ago.


Question: When was the concept of history invented?

History of mathematics

They used the arrow editorial, which was later adopted by the peoples who ruled the region.


Question: When was the concept of history invented?

History of mathematics

Instead of the tensystem, a 60 system was in use.


Question: When was the concept of history invented?

History of mathematics

The choice had been made apparently consciously because 60 is divisible by many different numbers and thus convenient for computation.


Question: When was the concept of history invented?

History of mathematics

However, the Babylonians used the tenth system as a subsystem, meaning chapters 1—59 were formed from characters of ones and tens.


Question: When was the concept of history invented?

History of mathematics

[7] [8] Around 2500 BC.


Question: When was the concept of history invented?

History of mathematics

also began to denote numbers with signs in the arrow editorial, so all numbers were expressed by horizontal and vertical wedges.


Question: When was the concept of history invented?

History of mathematics

The low number of signs may have been one of the reasons that around 4000 years ago placeholding was first introduced in the area.


Question: When was the concept of history invented?

History of mathematics

Ones were marked by vertical wedges and dozens by horizontal ones.


Question: When was the concept of history invented?

History of mathematics

The same characters also indicated the other potencies of the stock number, so, for example, 4862=3600+21·60+2 was denoted Y →→Y YY.


Question: When was the concept of history invented?

History of mathematics

[7] This was a significant advance over the Egyptian method of notation, particularly because it also extended to negative powers of the strain number, and thus the notation was as effective as the decimal system in use today.


Question: When was the concept of history invented?

History of mathematics

The only shortcoming was zero, which was not present at all to begin with.


Question: When was the concept of history invented?

History of mathematics

3rd-century BCE


Question: When was the concept of history invented?

History of mathematics

However, it began to be used for the zero in the middle of the chapter, but the zero at the end of the chapter was not marked in any way.


Question: When was the concept of history invented?

History of mathematics

The magnitude of the figure therefore came to be understood out of context.


Question: When was the concept of history invented?

History of mathematics

[9] The benefits of the Babylonians” reading system were most clearly evident in the accuracy of their approximations.


Question: When was the concept of history invented?

History of mathematics

Their value for the square root of two was 1.414222, which is correct to five-digit accuracy.


Question: When was the concept of history invented?

History of mathematics

For calculating the square root, the Babylonians had a general method based on iteration.


Question: When was the concept of history invented?

History of mathematics

However, like Egyptian mathematicians, the Babylonians did not make a clear distinction between an approximation and an exact value.


Question: When was the concept of history invented?

History of mathematics

Thus, a good approximation was enough for them, and the Babylonians are not known to have studied the endless sets resulting from the iteration method.


Question: When was the concept of history invented?

History of mathematics

However, they apparently knew how to compute the sum of a finite geometric series and knew how to deal with finite sets anyway.


Question: When was the concept of history invented?

History of mathematics

Preserved clay tables have a lot of different tables that facilitate counting.


Question: When was the concept of history invented?

History of mathematics

The Babylonians have been marking up inverted figures tables and number potencies, and made logarithm tables that have been exploited in practice for things like interest bills.


Question: When was the concept of history invented?

History of mathematics

For the numbers missing from the table, they have calculated values by interpolation.


Question: When was the concept of history invented?

History of mathematics

[10] In equation solution, the Babylonians advanced considerably beyond the Egyptians.


Question: When was the concept of history invented?

History of mathematics

They learn to solve all second-order equations with at least one positive root.


Question: When was the concept of history invented?

History of mathematics

The sophistication of their algebra is shown by them solving second-order equations of the form ax²+bx+c=0 using the rank method by multiplying both sides by a and denoting ax=y.


Question: When was the concept of history invented?

History of mathematics

Similarly, they knew how to solve equations reversible to the second degree, such as x8+bx4+c=0.


Question: When was the concept of history invented?

History of mathematics

The Babylonians also solved at least three-thermal third-order equations.


Question: When was the concept of history invented?

History of mathematics

There is no definite evidence for the solution of the perfect third order equation.


Question: When was the concept of history invented?

History of mathematics

What makes it difficult to work out the level of mathematics is that the Babylonians did not write down their solution methods as formulas of any kind, but as practical, operating instructions bound to certain numbers.


Question: When was the concept of history invented?

History of mathematics

Therefore, it is sometimes impossible to know whether they have known the general solution to the problem or just a specific case.


Question: When was the concept of history invented?

History of mathematics

At least for the diagonal of the square, they have known that in every square the ratio of diagonal to side is √2.


Question: When was the concept of history invented?

History of mathematics

[10] The geometry of the Babylonians was more advanced than the Egyptians, although they mainly viewed it as an application of algebra.


Question: When was the concept of history invented?

History of mathematics

Thus, no geometric proofs exist.


Question: When was the concept of history invented?

History of mathematics

Anyway, their evidence is limited to the fact that the claim was proven by calculation correct.


Question: When was the concept of history invented?

History of mathematics

The Babylonians were the first to develop the Pythagorean theorem.


Question: When was the concept of history invented?

History of mathematics

Furthermore, they were ahead of the Egyptians in that they could calculate areas of patterns and thirst lengths by utilizing uniform patterns.


Question: When was the concept of history invented?

History of mathematics

No actual trigonometry the Babylonians had, but tabulated values have been found in clay tables corresponding to the square of secant with angle values of 31°—45°.


Question: When was the concept of history invented?

History of mathematics

Tangent values have probably been tabulated, too, but they have not survived.


Question: When was the concept of history invented?

History of mathematics

Still, the angle was not considered to be measurable large; instead, the values are related to the ratios of the sides of certain triangles, and the secant or tangent has thus not been in use as an abstract function.


Question: When was the concept of history invented?

History of mathematics

Perhaps the most significant reform of the Babylonians in terms of the development of mathematics was mathematics partially disconnected from practice.


Question: When was the concept of history invented?

History of mathematics

For some of the calculations, it is impossible to imagine applications of that time, so Babylonian mathematicians are the first to study mathematics because of its own.


Question: When was the concept of history invented?

History of mathematics

[10] Ancient mathematics (600 BC.—500 share.)


Question: When was the concept of history invented?

History of mathematics

Greek culture favored the practice of sciences, especially philosophy, logic and mathematics.


Question: When was the concept of history invented?

History of mathematics

Therefore, mathematics developed in ancient Greece to a whole new level compared to the pre-Hellenic period.


Question: When was the concept of history invented?

History of mathematics

The Greeks made many important individual mathematical discoveries, but most important was the transformation of mathematics into its own discipline as it is known today.


Question: When was the concept of history invented?

History of mathematics

In Babylonia and Egypt, mathematics had been mainly practical.


Question: When was the concept of history invented?

History of mathematics

It was not outlined as an abstract logical system in which certain axioms, namely basic theorems and the rules derived from them, are valid.


Question: When was the concept of history invented?

History of mathematics

This kind of thought pattern arose in ancient Greece.


Question: When was the concept of history invented?

History of mathematics

[11] Hellenic period (600—300 BCE)


Question: When was the concept of history invented?

History of mathematics

7th century B.C.


Question: When was the concept of history invented?

History of mathematics

since then, the Greeks had begun to establish settlements along the Mediterranean and Black Sea coasts.


Question: When was the concept of history invented?

History of mathematics

This also brought further contacts with the old centres of mathematics, Babylonia and Egypt, and was apparently one of the reasons for the rapid development of mathematics.


Question: When was the concept of history invented?

History of mathematics

The first Greek mathematicians known by name were Thales (circa 624—548BCE.)


Question: When was the concept of history invented?

History of mathematics

and Pythagoras (circa 580—500BC.).


Question: When was the concept of history invented?

History of mathematics

Of their works none have survived, but many later mathematicians refer to them in their works.


Question: When was the concept of history invented?

History of mathematics

However, it is debatable which of all the inventions usually put in their names were actually developed by them themselves.


Question: When was the concept of history invented?

History of mathematics

Thalee is usually credited with developing geometric deductive reasoning.


Question: When was the concept of history invented?

History of mathematics

Pythagoras and his followers established a school according to which everything was to be represented by integers and their ratios.


Question: When was the concept of history invented?

History of mathematics

They were thus the first to seek to describe nature in a regular way through mathematics.


Question: When was the concept of history invented?

History of mathematics

Pythagoras observed how the length of an oscillating tongue affects pitch and studied the proportions the lengths of the languages should be in order to produce tunes belonging to a single octave.


Question: When was the concept of history invented?

History of mathematics

They also introduced the concepts of prime number and golden-cut.


Question: When was the concept of history invented?

History of mathematics

The Pythagorean worship of figures led to the study of different numbers queues, and certain figures were considered “more valuable” than others.


Question: When was the concept of history invented?

History of mathematics

This led to them distinguishing between pure mathematics and logistics focusing on calculus engineering.


Question: When was the concept of history invented?

History of mathematics

This may have slowed the development of the way figures were notated when practical calculation was considered inferior.


Question: When was the concept of history invented?

History of mathematics

The Greeks marked figures initially using a system resembling Roman numerals.


Question: When was the concept of history invented?

History of mathematics

No later than the 4th century BC.


Question: When was the concept of history invented?

History of mathematics

switched to an Ionian method of notation, which resembled a place system.


Question: When was the concept of history invented?

History of mathematics

The complete place system never began to be used, and the Ionian notation was not used for fractions.


Question: When was the concept of history invented?

History of mathematics

The Pythagoreans considered them to be a ratio of two integers rather than discrete numbers placed between integers in magnitude.


Question: When was the concept of history invented?

History of mathematics

[12] In the 4th century BCE.


Question: When was the concept of history invented?

History of mathematics

Greek mathematics spread across the Hellenic world to southern Italy, Thrace and Lesser Asia.


Question: When was the concept of history invented?

History of mathematics

Although many notable mathematicians lived at the time, none of the texts written by them themselves have survived.


Question: When was the concept of history invented?

History of mathematics

Three classical problems of geometry arose at that time, squaring the circle, duplication of the cube, and angle triangulation using a harp and ruler alone.


Question: When was the concept of history invented?

History of mathematics

Although the Greeks did not solve the problems, studying them led to many new discoveries.


Question: When was the concept of history invented?

History of mathematics

In particular, the difference between the concepts of exact value and approximation was specified.


Question: When was the concept of history invented?

History of mathematics

The Greeks were the first to understand that an accurate approximation never equals an exact value.


Question: When was the concept of history invented?

History of mathematics

[13] Hippocrates Chhiosite (circa 470—410BCE.


Question: When was the concept of history invented?

History of mathematics

) [14], when studying circle squaring, succeeded in squaring crests of a particular shape, and was thus the first to accurately calculate the area of a curve-line pattern.


Question: When was the concept of history invented?

History of mathematics

Athenian Hippias (circa 460—400BC.


Question: When was the concept of history invented?

History of mathematics

) [15] invented a way to perform angular triangulation using a curve called quadratrix as an auxiliary.


Question: When was the concept of history invented?

History of mathematics

Since the curve could not be created using a harp and ruler, the solution was not acceptable.


Question: When was the concept of history invented?

History of mathematics

Hippias, however, had invented the first curve, which was not a circle arch or straight.


Question: When was the concept of history invented?

History of mathematics

The first geometric solution for the duplication of the cube was put forward by the Tarentumian Arkhytas.


Question: When was the concept of history invented?

History of mathematics

His solution was based on the intersection of a torus formed by a cone, cylinder and circle that would be conveniently drawn according to the cube to be duplicated, which determined the place of the tip of the new cube.


Question: When was the concept of history invented?

History of mathematics

The solution shows that Greek mathematics was at a very abstract level, considering that they did not have an analytical geometry or even a coordinate system like today.


Question: When was the concept of history invented?

History of mathematics

[13] The Pythagorean idea of a world dominated by integers and their relations collapsed in the 4th century BCE.


Question: When was the concept of history invented?

History of mathematics

At that time, it was successful in proving that, for example, the side and diagonal of a square are codimensionless, that is, expressed in modern terms, their relation is an irrational number.


Question: When was the concept of history invented?

History of mathematics

Honor for this invention is often given to Hippasos (circa 530—450 BCE.


Question: When was the concept of history invented?

History of mathematics

) [16], although there is no certainty on the matter.


Question: When was the concept of history invented?

History of mathematics

The ratio of the golden cut was also proven to be an irrational number.


Question: When was the concept of history invented?

History of mathematics

Together with Zenon (490—425 BCE.


Question: When was the concept of history invented?

History of mathematics

With the paradoxes developed by) [17], this led to the fact that geometry, rather than figures, began to be considered as the basis of everything.


Question: When was the concept of history invented?

History of mathematics

Figures were considered to have a discrete character, and Zenon showed that describing space as discrete causes contradictions.


Question: When was the concept of history invented?

History of mathematics

Thus, the figures could not describe the real world of continuous greats.


Question: When was the concept of history invented?

History of mathematics

Largely as a result of this, geometric algebra emerged, in which a geometric proof is sought for theorems in algebra.


Question: When was the concept of history invented?

History of mathematics

No calculation involving the ratio of codimensionless numbers could be performed; instead, a geometric construct had to be made for its solution.


Question: When was the concept of history invented?

History of mathematics

[18] For example, second-order equations and square root values began to be solved geometrically.


Question: When was the concept of history invented?

History of mathematics

[19] In the 3rd century BCE.


Question: When was the concept of history invented?

History of mathematics

Plato (427—347 BC)


Question: When was the concept of history invented?

History of mathematics

founded his Academy and thus supported mathematicians and the development of mathematics.


Question: When was the concept of history invented?

History of mathematics

He himself did not end up with significant results, but sought to clarify the definitions and methods of proof in mathematics.


Question: When was the concept of history invented?

History of mathematics

Plato applied his doctrine of ideas to mathematics, stressing that geometry does not deal with patterns drawn but the ideas they represent.


Question: When was the concept of history invented?

History of mathematics

Thus mathematics became increasingly clear from practice into a separate science.


Question: When was the concept of history invented?

History of mathematics

Eudoxos, who studied at Plato's Academy (circa 408—335 BCE)


Question: When was the concept of history invented?

History of mathematics

rose to be the most prominent mathematician of the time.


Question: When was the concept of history invented?

History of mathematics

He solved the problem posed by codimensionless largesse.


Question: When was the concept of history invented?

History of mathematics

The difficulty had been the magnitude of the ratio of two codimensionless numbers versus the ratio of two integers (i.e., in modern terms, the ratio of an irrational number to a rational number), but Eudoxos's new definition of the relationship solved the problem.


Question: When was the concept of history invented?

History of mathematics

[20] The idea of his definition is very close to the definition of real numbers introduced by Dedekind in the 19th century.


Question: When was the concept of history invented?

History of mathematics

[21] Eudoxos achieved another significant result when he developed an exhaustion method preceding integral calculus, which could accurately calculate fields of curve-line patterns.


Question: When was the concept of history invented?

History of mathematics

Even before him, for example, Democritos had attempted to calculate volumes of pieces using infinitesimal [22], but it was not until Eudoxos developed an exact of computation with infinitesimal quantities.


Question: When was the concept of history invented?

History of mathematics

He succeeded in proving the theorem that by subtracting from the given great at least half, from the remaining great at least half, and continuing the process, one obtains a number smaller than any number.


Question: When was the concept of history invented?

History of mathematics

This means in current notation lim n → ∞ M (1 − r) n = 0 {\ displaystyle\ lim _ {n\ to\ infty} M (1-r) ^ {n} =0}, where M {\ displaystyle M} is the original suure and 1/2 ≤ r < 1 {\ displaystyle 1/2\ leq r<1}.


Question: When was the concept of history invented?

History of mathematics

Eudoxos' pupil Menaikhmos discovered the cone cuts while studying the duplication of the cube.


Question: When was the concept of history invented?

History of mathematics

[23] Hellenistic period (300—100 BCE)


Question: When was the concept of history invented?

History of mathematics

In the late 3rd century BCE.


Question: When was the concept of history invented?

History of mathematics

Alexander the Great had united Greece, Egypt and the entire Middle East under his rule.


Question: When was the concept of history invented?

History of mathematics

As Hellenic and Eastern culture merged with each other, a new Hellenistic culture emerged.


Question: When was the concept of history invented?

History of mathematics

This influenced the development of mathematics such that the center of mathematics moved from Greece to Alexandria.


Question: When was the concept of history invented?

History of mathematics

The Hellenistic period is also said to be the Alexandrian period, and is considered the culmination of Greek mathematics.


Question: When was the concept of history invented?

History of mathematics

[24] It was during this period that the famous mathematicians Eucliides (325—265 BCE) lived.


Question: When was the concept of history invented?

History of mathematics

) [25], Archimedes (287—212 BC)


Question: When was the concept of history invented?

History of mathematics

and Apollonios Pergan (circa 262—190 BCE).


Question: When was the concept of history invented?

History of mathematics

Eucleides is best known for his work Stoikheia, Alkeet¨.


Question: When was the concept of history invented?

History of mathematics

The work is also known by its Latin name Elementa.


Question: When was the concept of history invented?

History of mathematics

It is the main source of information on ancient Greek mathematics.


Question: When was the concept of history invented?

History of mathematics

Beginners is, as its name suggests, a textbook on the basics of mathematics, and does not deal with the most advanced mathematics of its time.


Question: When was the concept of history invented?

History of mathematics

Eucleides has written his work on the basis of previous studies, and probably very little of its content is developed by him himself.


Question: When was the concept of history invented?

History of mathematics

The merit of Eucliide lies in the logical structure of the book and in the quest for a clear representation of the fundamentals of mathematics, starting from certain axioms.


Question: When was the concept of history invented?

History of mathematics

Although his logic does not meet the current standards of punctuality, it was entirely adequate for the mathematicians of antiquity.


Question: When was the concept of history invented?

History of mathematics

Composed of 13 books, Elementa begins with plane geometry, incorporates the theory of comparisons developed on the basis of Eudoxos's definition of the relationship and the method of exhaustion, deals with number theory, and ends with the treatment of Plato's paragraphs.


Question: When was the concept of history invented?

History of mathematics

Eucleides wrote other works that contained more of his own research, but these have mostly disappeared.


Question: When was the concept of history invented?

History of mathematics

Citation by other sources suggested that he had studied at least cone cuts and developed some form of analytical geometry.


Question: When was the concept of history invented?

History of mathematics

[26] Archimedes was not only a mathematician, but also an inventor and the first physicist in history to use mathematics as a starting point.


Question: When was the concept of history invented?

History of mathematics

With the exception of the Pythagorean theory of the influence of language length on pitch, all physics, until Archimedes, had been speculative and philosophical.


Question: When was the concept of history invented?

History of mathematics

Using mathematics, Archimedes explained the law of lift and lever by which he could calculate the priorities of more complex pieces.


Question: When was the concept of history invented?

History of mathematics

By combining these, he was able to calculate how bodies and boats of different shapes float and thus laid the foundation of hydrostatics.


Question: When was the concept of history invented?

History of mathematics

Using his lever law, Archimedes developed the method of exhaustion at its peak, calculating, for example, the area of the sphere segment and the area left inside the spiral.


Question: When was the concept of history invented?

History of mathematics

Archimedes was also the first to succeed in solving the real-valued roots of the general tertiary equation.


Question: When was the concept of history invented?

History of mathematics

[27] Apollonio can be considered the greatest geometrician of antiquity.


Question: When was the concept of history invented?

History of mathematics

Unlike Eucleides, he developed a huge number of proofs and new theorems of geometry himself.


Question: When was the concept of history invented?

History of mathematics

Most of his work has been lost, but the most important, from the cone cuts, has been preserved.


Question: When was the concept of history invented?

History of mathematics

In it, Apollonios shows how cone cuts can be processed in the plane and how all the taper cuts can be obtained from the same cone by changing the cutting angle.


Question: When was the concept of history invented?

History of mathematics

He is the first to use a coordinate system, but does not consider it an independent system, instead attaching to each cone cut as the diameter and tangent to the curve of the coordinate system.


Question: When was the concept of history invented?

History of mathematics

A good example of Apollonios's other geometric work is the problem of Apollonios named after him, whose hardest part, three circles tangential to circles, Apollonius himself could not solve.


Question: When was the concept of history invented?

History of mathematics

In addition, Apollonius's merits include the idea of describing the motion of planets with epicycles.


Question: When was the concept of history invented?

History of mathematics

[28] Roman period (100 BC.—529) Greece and the Aegean region were annexed in the 10th century BCE.


Question: When was the concept of history invented?

History of mathematics

The Roman Empire.


Question: When was the concept of history invented?

History of mathematics

At the same time, the decline of Greek mathematics and became more practical also began.


Question: When was the concept of history invented?

History of mathematics

Some scholars believe the reason for the recession was Rome's negative attitude towards the sciences.


Question: When was the concept of history invented?

History of mathematics

The practical trend was evident as the development of trigonometry to meet the needs of astronomy and other measurement.


Question: When was the concept of history invented?

History of mathematics

Trigonometry was especially developed by Hipparchus (180-125 BCE.


Question: When was the concept of history invented?

History of mathematics

), who established the division of the circle into 360 degrees, and Ptolemy (85—165) [29], who made trigonometric formulas using trigonometric tables at intervals of a quarter of degree.


Question: When was the concept of history invented?

History of mathematics

The tables were published in his most notable work in Almagest.


Question: When was the concept of history invented?

History of mathematics

The Greeks did not use trigonometric functions in the same sense as they do today, but for them the values of the functions were integrally related to the tendon of the circle corresponding to a given angle.


Question: When was the concept of history invented?

History of mathematics

The Greeks were also familiar with all the major trigonometric formulas in use today, but used them in geometric form as different formulas for the tendons of the circle.


Question: When was the concept of history invented?

History of mathematics

[30] Although mathematics did not interest Rome or the Romans, after a quieter period Greek mathematics rose to a new heyday in the 200th century.


Question: When was the concept of history invented?

History of mathematics

At that time, interest in number theory was revived after geometry was almost the only branch of mathematics studied for a long time.


Question: When was the concept of history invented?

History of mathematics

The reason for this was the interest raised by Neo-Platonism in Pythagoreans' ideas about a world dominated by figures and the interest in algebra that spread in Babylonia with the Roman conquests.


Question: When was the concept of history invented?

History of mathematics

The most prominent representative of the new trend was Diophantos (around 200—284) [31].


Question: When was the concept of history invented?

History of mathematics

He is sometimes referred to as the father of algebra because he established the use of symbols in mathematics instead of the verbal instructions in use up to that point.


Question: When was the concept of history invented?

History of mathematics

Diophantos studied indetermined equations and solved them exactly, though he was not interested in finding all possible solutions.


Question: When was the concept of history invented?

History of mathematics

Instead of precise logic, Diophantos concentrated on solving problems in practice.


Question: When was the concept of history invented?

History of mathematics

[32] In the field of geometry, the new rise of mathematics culminated in Pappos (290—350) [33].


Question: When was the concept of history invented?

History of mathematics

He was the last notable geometrician of antiquity.


Question: When was the concept of history invented?

History of mathematics

The most important of his publications was The Collection (Synagoge), in which he seeks to bring together the expertise of geometry at the time.


Question: When was the concept of history invented?

History of mathematics

Due to its references, the work is a valuable source for previous developments in mathematics.


Question: When was the concept of history invented?

History of mathematics

In addition, it contains Pappos's own research, mainly generalizations of previous geometric sentences and new proofs.


Question: When was the concept of history invented?

History of mathematics

Furthermore, he posits the hypothesis that the three classical problems of geometry are not solvable by harp and ruler.


Question: When was the concept of history invented?

History of mathematics

It was not until modern algebra that allowed the hypothesis to be proven.


Question: When was the concept of history invented?

History of mathematics

Pappos also proves in his book a theorem known as the Pappos-Guldin Theorem.


Question: When was the concept of history invented?

History of mathematics

[34] After Pappos, the development of mathematics in Europe ceased for centuries.


Question: When was the concept of history invented?

History of mathematics

After him, only the most advanced mathematicians were able to fully understand the texts of antiquity and were content only to comment and explain them.


Question: When was the concept of history invented?

History of mathematics

Alexandria's time as a centre of mathematics came to an end in 415 when Hypatia, who had defended old Hellenic values and paganism, was murdered by fanatical Christians, who was a learned mathematician.


Question: When was the concept of history invented?

History of mathematics

Admittedly, the university, which was associated with the Library of Alexandria, had been closed even earlier, but the murder frightened other scholars who left the city.


Question: When was the concept of history invented?

History of mathematics

[35] In Western Rome, the practice of mathematics had never attained significant status, and with the collapse of the empire, confusing conditions gave no opportunity for university activities.


Question: When was the concept of history invented?

History of mathematics

Most distantly ancient mathematics lived in Byzantium, where, for example, Eutokios still made significant commentaries on the works of Archimedes and Apollonios in the early 5th century.


Question: When was the concept of history invented?

History of mathematics

In Byzantium, Plato's Academy had survived as the centre of mathematics, but Emperor Justinian I abolished the college in 527, seeing its Neo-Platonist philosophy as a threat to Christianity.


Question: When was the concept of history invented?

History of mathematics

[36] Native American mathematics (500 BC.—1500) Mathematics did not have time to develop in the Americas well before the arrival of Europeans.


Question: When was the concept of history invented?

History of mathematics

Many indigenous languages do not even have two larger number words; they are replaced by the concept of many.


Question: When was the concept of history invented?

History of mathematics

In languages where there were more number words, the three, ten or 20 system was most commonly used.


Question: When was the concept of history invented?

History of mathematics

The most advanced processing of chapters developed in the Inca State and the developed Indian states of Central America.


Question: When was the concept of history invented?

History of mathematics

However, actual mathematics can only be talked about as far as the Mayan is concerned.


Question: When was the concept of history invented?

History of mathematics

Around the 5th century BCE.


Question: When was the concept of history invented?

History of mathematics

the Mayan numeral system introduced was the first complete place system in the world, and the Mayans thus used zero as the first in the world.


Question: When was the concept of history invented?

History of mathematics

In other respects, however, the Mayans were not on the same level as their contemporaries in Egypt or Mesopotamia.


Question: When was the concept of history invented?

History of mathematics

There was no algebra of any kind and mathematics was only used for practical purposes.


Question: When was the concept of history invented?

History of mathematics

The main areas of application were astronomy, time calculation, and station zoning planning.


Question: When was the concept of history invented?

History of mathematics

The Mayans used geometry to determine the dimensions and location of buildings as advantageous to religion.


Question: When was the concept of history invented?

History of mathematics

The Mayan period calculation was very accurate and based on accurate astronomical observations.


Question: When was the concept of history invented?

History of mathematics

They measured, for example, the length of a synodic month with an accuracy of 23 seconds.


Question: When was the concept of history invented?

History of mathematics

[37], [38] Chinese mathematics (300 BC.—1600) Mathematics developed in China without the exchange of knowledge with other high cultures until at least the beginning of the period, later contacts especially with India are only fragmented and the direction of the flow of information is unclear.


Question: When was the concept of history invented?

History of mathematics

As in the Hellenic region, in China, much of the original sources have been destroyed, partly between the adolescence periods associated with many dynamish exchanges.


Question: When was the concept of history invented?

History of mathematics

The oldest surviving work by Zhou Bi Suan Jing is most likely from the 3rd century BCE.


Question: When was the concept of history invented?

History of mathematics

It deals with astronomical measurements, elementary geometry, and fractional calculation.


Question: When was the concept of history invented?

History of mathematics

More famous than this dates to around 250 BCE.


Question: When was the concept of history invented?

History of mathematics

The Nine Chapters, which is apparently the earliest work to use negative figures.


Question: When was the concept of history invented?

History of mathematics

Neither of the works maintains the logical precision of Greek treatises, but resembles collections of problems made in Babylonia and Egypt, where tasks relate to practical measurements.


Question: When was the concept of history invented?

History of mathematics

[39] There was a ten-position system in China for hundreds of years before the beginning of the period, but zero was not introduced until the 7th century.


Question: When was the concept of history invented?

History of mathematics

Fractions were also marked by a decimal system.


Question: When was the concept of history invented?

History of mathematics

In the 2000s, share.


Question: When was the concept of history invented?

History of mathematics

In addition to geometric problems, Liu Hui dealt with groups of equations and solved equations of higher order in a manner similar to the operation now known as the Horner Method.


Question: When was the concept of history invented?

History of mathematics

Zu Chongzhi (430—501) calculated the value of silicon with astonishing accuracy (3,1415926<π<3.1415927).


Question: When was the concept of history invented?

History of mathematics

However, the peak of Chinese mathematics was not reached until the 13th century.


Question: When was the concept of history invented?

History of mathematics

The most prominent mathematician of the time was Zhu Shijie, who presents in his book The Precious Mirror of the Four Elements today the table known as Pascal's Triangle and even 14th-degree equations iterative approximate solution processes resembling Horner's method.


Question: When was the concept of history invented?

History of mathematics

Another mathematician of the era, Yang Hui, developed magic squares of 10 times 10 size, for the processing of which the Chinese had developed methods similar to matrix operations.


Question: When was the concept of history invented?

History of mathematics

The third notable mathematician was Qin Jiushao.


Question: When was the concept of history invented?

History of mathematics

After the 13th century, the development of Chinese mathematics slowed down, and by the 15th century it had fallen well behind the level of Arabic and European mathematics.


Question: When was the concept of history invented?

History of mathematics

[40] Indian mathematics (0—1600) The examination of early mathematical developments in India is difficult due to the lack of sources and the imaginary nature of the ancient Hindu period.


Question: When was the concept of history invented?

History of mathematics

No sources exist from the period of the earliest Indus culture in the area.


Question: When was the concept of history invented?

History of mathematics

The first surviving written product is Sulvasutra, a collection of geometric knowledge, the genesis of which is dated to the years 700 BC.—100 share.


Question: When was the concept of history invented?

History of mathematics

It deals mostly with planar geometry related to surveying and has Babylonian influences.


Question: When was the concept of history invented?

History of mathematics

The following sources are the Siddhantas from the period of the Gupta Empire between the 300th and 5th centuries.


Question: When was the concept of history invented?

History of mathematics

They are collections of unproven mathematical rules written in the form of epic stanzas, which also contain incorrect formulas for volumes of paragraphs, for example.


Question: When was the concept of history invented?

History of mathematics

Unprovability and intuitiveness are characteristics typical of Indian mathematics from later times.


Question: When was the concept of history invented?

History of mathematics

Greek influences are discernible in the Siddhantos, but Indian mathematicians have transformed them into a form characteristic of themselves.


Question: When was the concept of history invented?

History of mathematics

A good example of this is the most significant anti of the works, the current form of trigonometric functions.


Question: When was the concept of history invented?

History of mathematics

The Greeks had used the ratio of the tendon of the circle to the central angle, but the Indians adopted the tendon half as opposed to the central corner half.


Question: When was the concept of history invented?

History of mathematics

[41] Aryabhatiya, a prominent mathematician, expanded on the use of trigonometric functions in his work published in 499.


Question: When was the concept of history invented?

History of mathematics

However, the most significant aspect of the work is its section dealing with the Indian reading system.


Question: When was the concept of history invented?

History of mathematics

It shows Indians to have been the first to adopt the modern method of notation of integers, now called Arabic numerals.


Question: When was the concept of history invented?

History of mathematics

The affectionate was a complete place system with a base number of 10 and only ten characters used to mark the numbers.


Question: When was the concept of history invented?

History of mathematics

None of these three features had developed in India, but it was there that they were first combined.


Question: When was the concept of history invented?

History of mathematics

The most significant change in relation to the Ionian marking of the Greeks was the addition of zero, moreover, due to the place system, unnecessary own marks for tens and hundreds were omitted.


Question: When was the concept of history invented?

History of mathematics

Accurate timing of the genesis of zero is impossible, and apparently it was initially marked only with an empty spot.


Question: When was the concept of history invented?

History of mathematics

The earliest undisputed zero has been found in an inscription dating back to 876.


Question: When was the concept of history invented?

History of mathematics

However, the Indians used the place system only for integer notation.


Question: When was the concept of history invented?

History of mathematics

[42] Brahmagupta, the foremost Indian mathematician of the 6th century, was the first to present the form of a general solution for the Diophantos equation of ax+by=c.


Question: When was the concept of history invented?

History of mathematics

Another notable achievement is the first systematic representation for the arithmetics of negative numbers and zero, though Brahmagupta incorrectly posits that 0/0=0, for the general case x/0 he does not take a position.


Question: When was the concept of history invented?

History of mathematics

In addition, he presents numerous results of very different levels relating to geometry and equation solving, some of which are completely incorrect.


Question: When was the concept of history invented?

History of mathematics

After a quieter period, Indian mathematics reached its peak in the 12th century.


Question: When was the concept of history invented?

History of mathematics

Bhāskara II (1114—1185), who lived at the time, expanded the calculus rules for Brahmagupta zero by stating that x/0=infinity.


Question: When was the concept of history invented?

History of mathematics

The limit values were not spoken by the Indians, however, and Bhaskara defined 0•a/0=a.


Question: When was the concept of history invented?

History of mathematics

In addition, he presented solutions to Pell's equation.


Question: When was the concept of history invented?

History of mathematics

[43] Arabic mathematics (600—1600) After the dissolution of the Roman Empire and the reintroduction of Hellenistic science, the Islamic kingdom founded by Muhammad was of essential importance as the preserver of ancient knowledge and the creator of new knowledge.


Question: When was the concept of history invented?

History of mathematics

The Arabs who lived as nomads quickly embraced the achievements of Babylonian, Greek and Indian mathematicians, combining them and expanding the results.


Question: When was the concept of history invented?

History of mathematics

In the 750s, Caliph al-Mansur began to develop Baghdad, the capital of the kingdom, into a major centre of erudition, and old manuscripts began to be translated into Arabic.


Question: When was the concept of history invented?

History of mathematics

His successors, Harun al-Rašid and Al-Mamun, continued to popularise the sciences, and the latter founded the House of Wisdom in Baghdad, where scholars from all over the known world were gathered.


Question: When was the concept of history invented?

History of mathematics

Among the first notable mathematicians of the House of Wisdom was Al-Khwarizmi, who lived in the early 8th century, who wrote several works on mathematics and astronomy.


Question: When was the concept of history invented?

History of mathematics

Among the most important of his literary production are al-Jabr, who gave the name to algebra, as well as a book on the Indian reading system adopted by Arabs, known only from Latin called De number indorum.


Question: When was the concept of history invented?

History of mathematics

Of the two, due to the thoroughness of the latter and the subsequent wide spread in Europe, the Indian system began to be considered developed by Arabic, and numbers began to be called Arabic numerals.


Question: When was the concept of history invented?

History of mathematics

Thanks to al-Jabri, Al-Khwarizm can be considered the father of algebra in addition to Diophantos, as he dealt in it consistently and carefully with the calculation rules of integers and the solving of first and second order equations.


Question: When was the concept of history invented?

History of mathematics

In second-order equations, negative roots were not accepted as real solutions, although negative numbers were commonly used in Arabia.


Question: When was the concept of history invented?

History of mathematics

The work went through algebraic and geometric proofs of calculations alike, a testament to both Babylonian and Greek influences.


Question: When was the concept of history invented?

History of mathematics

[44] Another notable 8th-century mathematician Thabit ibn-Qurra was particularly distinguished in translating and commenting on the most advanced works of antiquity.


Question: When was the concept of history invented?

History of mathematics

He expanded and corrected sentences and proofs in areas such as number theory and the geometry of paraboloids.


Question: When was the concept of history invented?

History of mathematics

At the latest in his time in Arabia, the modern form of trigonometric functions used by Indians, rather than the old custom of the Greeks, had become well established.


Question: When was the concept of history invented?

History of mathematics

Trigonometry was further developed by Abu al-Wafa, who lived in the 9th century, who widely adopted, besides sine and cosine, other trigonometric functions and the unit circle, as well as proving numerous trigonometric identities.


Question: When was the concept of history invented?

History of mathematics

In the 10th century, Arabic science reached its peak.


Question: When was the concept of history invented?

History of mathematics

Known as the father of optics, Ibn-al-Haitham studied the passage of light and the structure of the eye.


Question: When was the concept of history invented?

History of mathematics

In them he applied and expanded the space geometric results associated with cone cuts of antiquity.


Question: When was the concept of history invented?

History of mathematics

ibn Yunus derived a formula for the input of two cosines.


Question: When was the concept of history invented?

History of mathematics

Also known as a poet, Omar Khaijam, a Persian, wrote a broader representation of algebra from al-Khawarizmi's work, which also included solving positive roots of third-order equations using the geometric method.


Question: When was the concept of history invented?

History of mathematics

He sought to narrow the division between numerical and geometric algebra, and did not study this solution of higher-order equations because there was no equivalent for them in reality.


Question: When was the concept of history invented?

History of mathematics

In addition, he sought to specify definitions of rational number, real number, and irrational number.


Question: When was the concept of history invented?

History of mathematics

Khaijam also presents the Pascal Triangle, also known in China at the time, whose origins are unclear.


Question: When was the concept of history invented?

History of mathematics

[45] After Khaijam in the 12th century, the level of science in the Islamic world began to decline along with the state dispersal.


Question: When was the concept of history invented?

History of mathematics

However, the level of mathematics did not suddenly drop.


Question: When was the concept of history invented?

History of mathematics

In the 13th century, the Persian Nasir al-Din al-Tusi studied geometry and trigonometry and produced the first systematic representation of spherical geometry.


Question: When was the concept of history invented?

History of mathematics

The last notable mathematician was al-Kashi, who lived in the 15th century, who became acquainted in Samarkand with the mathematical results of the Chinese.


Question: When was the concept of history invented?

History of mathematics

He is famous for his precise computational achievements.


Question: When was the concept of history invented?

History of mathematics

Using the Horner method he learned from the Chinese, he solved exact approximations for equations and calculated the value of pi to 16 decimal places.


Question: When was the concept of history invented?

History of mathematics

[46] Mathematics in medieval Europe (529—1450) Western Europe had poor opportunities for the practice of science after the dissolution of the Roman Empire.


Question: When was the concept of history invented?

History of mathematics

States did not invest in research, and erudition was concentrated in monasteries.


Question: When was the concept of history invented?

History of mathematics

Throughout the Middle Ages, scientific progress was slowed by the view of many Christian scholars about the needlessness of scientific research alongside religion.


Question: When was the concept of history invented?

History of mathematics

[47] In Byzantium, no similar political turmoil arose, and there the development of culture was not broken.


Question: When was the concept of history invented?

History of mathematics

Christianity slowed new research there too, but in monasteries commentaries were drawn up on works from antiquity and copied works.


Question: When was the concept of history invented?

History of mathematics

However, the growth of the importance of theology led to the fact that all mathematical achievements of antiquity were no longer understood.


Question: When was the concept of history invented?

History of mathematics

Thus, no significant new mathematical observations were made in Byzantium during the Middle Ages.


Question: When was the concept of history invented?

History of mathematics

[48] With the incorporation of much of Western Europe into the Frankish Empire by Charles the Great in the late 7th century, the level of erudition gradually began to take off.


Question: When was the concept of history invented?

History of mathematics

Charles the Great sought to develop the school institution of his kingdom and opened libraries in the main cities.


Question: When was the concept of history invented?

History of mathematics

The most famous scholar of the kingdom was the mathematician Alkuin Yorker, who was called from England.


Question: When was the concept of history invented?

History of mathematics

However, little mathematical works of antiquity were preserved or available in the West.


Question: When was the concept of history invented?

History of mathematics

Mathematics was still limited to the rudimentary of geometry and the maintenance of time calculation.


Question: When was the concept of history invented?

History of mathematics

Except for commentaries on Boëthius's works by Pope Sylvester I, who dabbled in mathematics, Western European mathematics did not much increase before the 12th century.


Question: When was the concept of history invented?

History of mathematics

[49] [50] In the 12th century, Europeans' contacts with the Arabic world increased and knowledge of the Arabic language spread to European scholars.


Question: When was the concept of history invented?

History of mathematics

The most important connection was Spain, where Toledo grew to be a major centre of erudition and translation work, but also through Sicily and Byzantium information about Arabia was gained.


Question: When was the concept of history invented?

History of mathematics

The first mathematical work translated from Arabic was Elementa in 1142, Other important translations made in the 12th century were the Almagest of Ptolemy and the Algebra of al-Khwarizm.


Question: When was the concept of history invented?

History of mathematics

Translations spread to universities, which began to be established in the 12th century with economic growth as social conditions stabilised.


Question: When was the concept of history invented?

History of mathematics

In particular, trigonometry achieved a strong position in Western Europe.


Question: When was the concept of history invented?

History of mathematics

With the translations, Indian numerals arrived in Europe.


Question: When was the concept of history invented?

History of mathematics

They gradually became widespread, as already Pope Sylvester I had used them in his writings [51], but it was not until the 13th century that they supplanted the use of Roman numerals in the circle of mathematicians.


Question: When was the concept of history invented?

History of mathematics

The introduction of Indian numerals was promoted by Fibonacci, the most prominent European mathematician of the 13th century, in his book Liber Abaci, in which he justified their advantages over Roman numerals.


Question: When was the concept of history invented?

History of mathematics

In mathematics he focused on algebra and number theory, guided by works translated from Arabic he studied indeterminate problems favoured by Diophantos in particular and calculated approximate solutions for third-order equations possibly using Horner's method learned from China through Arabic.


Question: When was the concept of history invented?

History of mathematics

Another noted 13th-century mathematician was Nemorarius, who was the first to present the power affecting a piece on a properly inclined plane, and wrote numerous semi-philosophical works on arithmetics and geometry.


Question: When was the concept of history invented?

History of mathematics

[51] In the 14th century, the universities of Oxford and Paris emerged as the most important centres for the study of mathematics in Europe.


Question: When was the concept of history invented?

History of mathematics

Although knowledge of mathematical methods was not yet at the same level as in ancient Greece and Arabia, numerous new ideas and perspectives emerged in 12th- and 14th-century Europe.


Question: When was the concept of history invented?

History of mathematics

Due to the lack of competence in geometry and algebra, research was oriented towards mathematics related to optics and kinematics that interested scholars.


Question: When was the concept of history invented?

History of mathematics

Thomas Bradwardine (1290—1349), when studying the laws of motion, introduced integer potencies and integer roots, and Parisian Nicole Oresme (1323—1382) extended this to general fractional potencies and put forward laws corresponding to the current rules for calculating potencies.


Question: When was the concept of history invented?

History of mathematics

Awkward notations and a flawed theory prevented him from developing the concept of irrational potencies.


Question: When was the concept of history invented?

History of mathematics

Oresme was the first to describe the variable large as a curve of the coordinate system.


Question: When was the concept of history invented?

History of mathematics

However, he confined himself to linear functions when describing velocity as a function of time, but posited that the distance traveled by a piece is obtained by calculating the area under the graph.


Question: When was the concept of history invented?

History of mathematics

He tried to extend his idea to functions of two variables as well, but in the absence of algebraic competence had to settle for pictorial outlines.


Question: When was the concept of history invented?

History of mathematics

Another new idea that emerged in the 14th century was the calculation of the sum of endless sets.


Question: When was the concept of history invented?

History of mathematics

Oresme was the first to show the harmonic series to disperse and computed the sums of many constricting sets.


Question: When was the concept of history invented?

History of mathematics

He can be considered to be the last notable European mathematician of the Middle Ages.


Question: When was the concept of history invented?

History of mathematics

In the mid-14th century, the Black Death spread to Europe, the Hundred Years' War began to strain France and England and the rise in the level of mathematics stopped.


Question: When was the concept of history invented?

History of mathematics

With the onset of the Renaissance in the 15th century, the center of research moved to Italy, Germany and Poland.


Question: When was the concept of history invented?

History of mathematics

[52] Renaissance mathematics (1450—1600) In the mid-15th century, Europe began to recover from the economic and demographic crisis caused by the Black Death.


Question: When was the concept of history invented?

History of mathematics

At the same time, a transformation called the Renaissance took place in the culture.


Question: When was the concept of history invented?

History of mathematics

The intensification of humanistic values and greater interest in secular matters contributed significantly to the development of all sciences, and the book printing invented by Johannes Gutenberg accelerated the dissemination of new works [53].


Question: When was the concept of history invented?

History of mathematics

Various elementary textbooks on arithmetics were first printed in Germany.


Question: When was the concept of history invented?

History of mathematics

[54] As recently as the Middle Ages, almost all formulas had been in verbal form, although abbreviations were used for the most common words.


Question: When was the concept of history invented?

History of mathematics

During the Renaissance, the use of symbols increased considerably in mathematical writing, and many of the basic notations in mathematics still in use date back to the 15th and 16th centuries.


Question: When was the concept of history invented?

History of mathematics

New markings gradually spread, and alternative methods of labelling were initially in use.


Question: When was the concept of history invented?

History of mathematics

[55] Nicolas Chuquet introduced in 1484 the current notation for potencies, in which the potency of the number x is expressed by the exponent written in its upper right corner [56].


Question: When was the concept of history invented?

History of mathematics

The symbols + and − that emerged in Germany replaced the abbreviations p and m previously in use.


Question: When was the concept of history invented?

History of mathematics

The new symbols appear for the first time in Johannes Widmann's Behende und hupsche Rechnung auf allen kauffmanschafft 1489.


Question: When was the concept of history invented?

History of mathematics

[57] The current method of notation of decimal parts and modern root notation also emerged in Germany at the beginning of the 16th century.


Question: When was the concept of history invented?

History of mathematics

[58] The equation mark depicting two parallel straight lines was invented by the Englishman Robert Recorde for his work published in 1551 [59].


Question: When was the concept of history invented?

History of mathematics

The 16th century also saw the use of the dividing line already learned by Fibonacci from the Arabians [60].


Question: When was the concept of history invented?

History of mathematics

As differences to the current method of notation, the unknown major was often marked with a dot or an upward arc of circles instead of a letter [61], and the symbols ×, > and < for multiplication and differentials were not yet in use [62].


Question: When was the concept of history invented?

History of mathematics

Algebra was the first field of mathematics in which European mathematicians far surpassed the achievements of scientists in antiquity and Arabia.


Question: When was the concept of history invented?

History of mathematics

Both Nicolas Chuquet and Italian Luca Pacioli published widespread compilation works on algebra at the end of the 15th century, and similar books were also published in Germany.


Question: When was the concept of history invented?

History of mathematics

However, the most significant work for the development of algebra was Ars magna published in 1545 by Geronimo Cardano, in which he presents the formula for solving equations of third and fourth order.


Question: When was the concept of history invented?

History of mathematics

He had not developed them himself; instead, for the third-order equation, the solution had been developed by Niccolo Tartaglia or Scipione dal Ferro, and for the fourth-order equation by Cardano's pupil Ludovico Ferrari.


Question: When was the concept of history invented?

History of mathematics

The solution formulas were not of great practical use, since equations of higher than the fourth order had already been able to be solved with approximate accuracy.


Question: When was the concept of history invented?

History of mathematics

Instead, solution formulas forced mathematicians to accept negative numbers and their square roots.


Question: When was the concept of history invented?

History of mathematics

It had previously been established that there was no solution for equations with imaginary roots.


Question: When was the concept of history invented?

History of mathematics

Now the square root of the negative number appeared in the solution formula for the third-order equation as a kind of intermediate step, even though the end result was a real number.