History of geometry
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, "The Elements" is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.
History of cartography
A vital contribution to mapping the reality of the world came with a scientific estimate of the circumference of the earth. This event has been described as the first scientific attempt to give geographical studies a mathematical basis. The man credited for this achievement was Eratosthenes (275–195 BC). As described by George Sarton, historian of science, "there was among them [Eratosthenes's contemporaries] a man of genius but as he was working in a new field they were too stupid to recognize him". His work, including "On the Measurement of the Earth" and "Geographica", has only survived in the writings of later philosophers such as Cleomedes and Strabo. He was a devoted geographer who set out to reform and perfect the map of the world. Eratosthenes argued that accurate mapping, even if in two dimensions only, depends upon the establishment of accurate linear measurements. He was the first to calculate the circumference of the Earth (within 0.5 percent accuracy) by calculating the heights of shadows at different points in Egypt at a given time. The first in Alexandria, the other further up the Nile, in the Ancient Egyptian city of Swenet (known in Greek as Syene) where reports of a well into which the sun shone only on the summer solstice, long existed. Proximity to the Tropic of Cancer being the dynamics creating the effect. He had the distance between the two shadows calculated and then their height. From this he determined the difference in angle between the two points and calculated how large a circle would be made by adding in the rest of the degrees to 360. His great achievement in the field of cartography was the use of a new technique of charting with meridians, his imaginary north–south lines, and parallels, his imaginary west–east lines. These axis lines were placed over the map of the earth with their origin in the city of Rhodes and divided the world into sectors. Then, Eratosthenes used these earth partitions to reference places on the map. He also divided Earth into five climatic regions: a torrid zone across the middle, two frigid zones at extreme north and south, and two temperate bands in between. He was also the first person to use the word "geography".