Who first landed the quadruple axel?
Figure skating jumps
Jumps are referred to by how many times the skater turns in the air. One revolution (one and a half for the Axel) is a "single" jump. Two revolutions (two and a half for the Axel) is a "double" jump. Three revolutions (three and a half for the Axel) is a "triple" jump. Four revolutions (four and a half for the Axel, although this has never been done in competition) is a "quadruple" or "quad" jump. The first triple jump landed in competition was a loop jump. It was landed by Dick Button in 1952. The first quadruple jump landed in competition was a toe loop jump. It was landed by Kurt Browning in 1988. Currently, men in world-class competition usually attempt a full set of triples and sometimes one or two quadruple jumps in their free skating programs. Triple Axels are rare for ladies, and quadruple jump attempts even more so.
Guo Zhengxin
Guo Zhengxin (, born August 1, 1979) is a Chinese former competitive figure skater who competed in men's singles. He finished 8th at the 1998 Winter Olympics and 7th at the World Figure Skating Championships the following year. He was the first skater to land two quadruple toe loops in the free skate.
Polar modulation
Polar modulation was originally developed by Thomas Edison in his 1874 quadruplex telegraph – this allowed 4 signals to be sent along a pair of lines, 2 in each direction. Sending a signal in each direction had already been accomplished earlier, and Edison found that by combining amplitude and phase modulation (i.e., by polar modulation), he could double this to 4 signals – hence, quadruplex.
John Baldwin (figure skater)
John Baldwin, Jr. (born October 18, 1973) is an American figure skater. With partner Rena Inoue, he is a two-time U.S. national champion. Inoue and Baldwin are the first skaters to perform a throw triple axel in competition.
Felix Baumgartner
Felix Baumgartner was born first of two boys on 20 April 1969 (his brother is Gerard), in Salzburg, Austria. As a child, he dreamed about flying and skydiving. In 1999, he claimed the world record for the highest parachute jump from a building when he jumped from the Petronas Towers in Kuala Lumpur, Malaysia. On 20 July 2003, Baumgartner became the first person to skydive across the English Channel using a specially made carbon fiber wing. Alban Geissler, who developed the SKYRAY carbon fiber wing with Christoph Aarns, suggested after Baumgartner's jump that the wing he used was a copy of two prototype SKYRAY wings sold to Red Bull (Baumgartner's sponsor) two years earlier.
Bell Airacobra I AH574
On 4 April 1945, "AH574" became part of aviation history when test pilot Captain Eric "Winkle" Brown landed it on the flight deck of HMS "Pretoria Castle"—the first carrier landing made by an aircraft with retractable tricycle gear—due to a declared emergency during initial trials for landings on rubber decks planned for future carriers.
Bobby Brown (freestyle skier)
Brown was the first to execute multiple variations of a triple flip or triple cork at a training session in Squaw Valley, California. He gained notoriety after winning both the SlopeStyle and Big Air events at Winter X Games XIV, registering a perfect score of 100 in the latter. Brown was the first person ever to have landed a Switch Double Misty 1440. He was one of the first skiers ever to have landed a Triple Cork 1440.
Cycloid
Constructing the tangent of the cycloid dates to August 1638 when Mersenne received unique methods from Roberval, Pierre de Fermat and René Descartes. Mersenne passed these results along to Galileo, who gave them to his students Torricelli and Viviana, who were able to produce a quadrature. This result and others were published by Torricelli in 1644, which is also the first printed work on the cycloid. This led to Roberval charging Torricelli with plagiarism, with the controversy cut short by Torricelli's early death in 1647.
Triple Crown of Cycling
Coppi was the first rider in the history of the sport to win the Giro d'Italia and the Tour de France in the same year which he did twice in 1949 and 1952. At the World road race championships in 1949 Coppi came third behind Rik Van Steenbergen of Belgium and Ferdi Kübler of Switzerland. Merckx was the first rider to win the triple crown but he had already come close to winning it in 1972 when he won both the Tour and the Giro, coming fourth in the World road race. After his disappointment, Merckx broke the world hour record several weeks later.
1991 Skate America
Harding performed a triple axel in her short program and free skating. She became the first woman to land the triple axel in the short program in major international competition.
Kepler triangle
Triangles with such ratios are named after the German mathematician and astronomer Johannes Kepler (1571–1630), who first demonstrated that this triangle is characterised by a ratio between its short side and hypotenuse equal to the golden ratio. Kepler triangles combine two key mathematical concepts—the Pythagorean theorem and the golden ratio—that fascinated Kepler deeply, as he expressed:
Composition algebra
The composition of sums of squares was noted by several early authors. Diophantus was aware of the identity involving the sum of two squares, now called the Brahmagupta–Fibonacci identity, which is also articulated as a property of Euclidean norms of complex numbers when multiplied. Leonhard Euler discussed the four-square identity in 1748, and it led W. R. Hamilton to construct his four-dimensional algebra of quaternions. In 1848 tessarines were described giving first light to bicomplex numbers.
Four wall paddleball
Four wall paddleball was invented in 1930 by Earl Riskey, a physical-education instructor and later Director of Intramural Sports at the University of Michigan. The paddleball trophy, awarded annually to the person who has done the most for the game, bears Riskey's name.
Dick Button
As reigning and defending champion, as well as being the first skater to perform a double axel and a flying camel, Button was under pressure to perform a new jump or spin every season. In 1949, he performed a 2Lo-2Lo combination. In 1950, he performed the 2Lo-2Lo-2Lo. In 1951, he performed a 2A-2Lo combination and a 2A-2A sequence. For the 1952 Winter Olympics, Button and Lussi began working on a triple jump. They settled on training the triple loop. Button landed it for the first time in practice in December 1951 at the Skating Club of Boston, and for the first time in exhibition in Vienna following the European Championships.
Torstein Horgmo
In the summer of 2010 he was the first to land a triple cork (three off axis flips and four full rotations before coming back in contact with the ground) off a 100 ft jump in Folgefonna, Norway. In the Winter X Games XV Horgmo landed an attempt of the triple cork in competition in the Big Air finals on January 28, 2011, winning a gold medal over Sebastien Toutant.
Brian Orser
In the 1984-1985 season, after Hamilton's retirement, Orser was seemingly poised to become the dominant champion. However, he had an imperfect worlds, and placed second to Alexander Fadeev, who also had the triple axel in his repertoire. Orser resolved to begin including two axels, not just one, in his free skate, in order to give himself an advantage over Fadeev. He finally won Worlds in 1987. At that competition he became the first skater at the World Championships to land two triple axels in the free skate and three in the same competition.
Double (basketball)
Quadruple-doubles have only been possible since the 1973–74 season, when the NBA started recording both blocked shots and steals. It is often speculated by observers that other all-time greats, namely Oscar Robertson (all time triple-doubles leader with 181), Wilt Chamberlain, Bill Russell and Jerry West could conceivably have had quadruple-doubles. West's biography at NBA.com claims that he once recorded an unofficial quadruple-double with 44 points, 12 rebounds, 10 assists and 10 blocks. A biography of Wilt Chamberlain claims that he also recorded an unofficial quadruple-double in Game 1 of the 1967 Eastern Division Finals against the Boston Celtics, when he had 24 points, 32 rebounds, 13 assists and 12 blocks.
Figure skating
The number of rotations performed in the air determines whether the jump is a single, double, triple, or quadruple (commonly known as a "quad"). The simplest jump begins with a waltz jump which can only be done in a half-leap and is not classified as a single, double, or triple jump. Senior-level male single skaters perform mostly triple and quadruple jumps in competition. Triple jumps other than the Axel are commonly performed by female single skaters. It is extremely rare for a female skater to land a quadruple jump; the only two female single skaters to be credited with quads in competition are Miki Ando, who landed the first quad Salchow in Dec 2002, and Alexandra Trusova, who landed the first quad Toe Loop (and only the second quad Salchow) in March 2018, both at the Junior level. Alexandra Trusova also was the first female to ever land 2 quadruple jumps in competition, the quad salchow and the quad toe loop. She was only 13 years old at the time.
TD Place Arena
Both Worlds provided memorable moments in sports. In 1978 Vern Taylor performed the first 'Triple axel' jump in competition. In 1984, the Canadian pairs champions Barbara Underhill and Paul Martini won the Championship in dramatic fashion:
Daryle Ward
After being called up from the Triple-A Nashville Sounds to replace Raúl Mondesí, Ward got off to a torrid start. On May 26, 2004, Ward, recalled from the Triple-A Nashville Sounds two weeks before, hit for the cycle and tied his career high with six RBI in the Pirates' 11-8 victory over the St. Louis Cardinals. Ward hit a two-run double in the first, an RBI triple in the fourth, golfed a three-run homer in the fifth and singled in the ninth. He was the first Pittsburgh player to hit for the cycle since Jason Kendall on May 19, 2000, against the Cardinals. It has been done 23 times in club history and 243 times since 1882.
Frank Bare Jr.
Frank Bare Jr. is an American freestyle skier. Bare was one of the sport's innovators and trained using a trampoline as well as on the aerials water ramps. In 1983, at Donner Ski Ranch, California, Bare performed the first quadruple somersault on skis. He did a triple twisting quadrupole back flip and did not wear a helmet. For nearly 20 years, no other skier performed a quadruple somersault onto snow.
Arthur Harold Stone
Arthur Harold Stone (30 September 1916 – 6 August 2000) was a British mathematician born in London, who worked mostly in topology. His wife was American mathematician Dorothy Maharam. His first paper dealt with squaring the square, he proved the Erdős–Stone theorem with Paul Erdős and is credited with the discovery of the first 2 flexagons, a trihexaflexagon and a hexahexaflexagon while he was a student at Princeton University in the USA in 1939. The Stone's metrization theorem has been named after him, and he was a member of a group of mathematicians who published pseudonymously as Blanche Descartes. He is not to be confused with American mathematician Marshall Harvey Stone.
1999 Skate America
Timothy Goebel made history by becoming the first person to land three quadruple jumps in one program. In the men's free skating, he landed a quad salchow, a quad toe loop in combination, and a quad toe loop as a solo jump.
6469 Armstrong
On 20 July 1969, Armstrong was one of the first two humans to land on the Moon, and the first person to walk on it, shortly followed by Buzz Aldrin, after whom the asteroid 6470 Aldrin is named. The minor planet 6471 Collins is named after the third crew member of the Apollo 11 mission. In 1966, Armstrong also conducted the first docking in space together with David Scott aboard Gemini 8. The asteroid's name was suggested by Czech astronomers Jana Tichá, Miloš Tichý and Zdeněk Moravec, who observed it during its 1995-opposition, shortly before being numbered. The lunar crater "Armstrong" is also named in his honor. The approved naming citation was published by the Minor Planet Center on 4 May 1999 ().
Quaternary cubic
A generic quaternary cubic can be written as a sum of 5 cubes of linear forms, unique up to multiplication by cube roots of unity. This was conjectured by Sylvester in 1851, and proven 10 years later by Clebsch. The union of the 5 planes where these 5 linear forms vanish is called the Sylvester pentahedron.
William Rowan Hamilton
Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional plane) to higher spatial dimensions. 
He failed to find a useful 3-dimensional system (in modern terminology, he failed to find a real, three-dimensional skew-field), but in working with four dimensions he created quaternions. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation
Projective line over a ring
Arthur Conway, one of the early adopters of relativity via biquaternion transformations, considered the quaternion-multiplicative-inverse transformation in his 1911 relativity study. In 1947 some elements of inversive quaternion geometry were described by P.G. Gormley in his paper "Stereographic projection and the linear fractional group of transformations of quaternions". In 1968 Isaak Yaglom's "Complex Numbers in Geometry" appeared in English, translated from Russian. There he uses P("D") to describe line geometry in the Euclidean plane and P("M") to describe it for Lobachevski's plane. Yaglom's text "A Simple Non-Euclidean Geometry" appeared in English in 1979. There in pages 174 to 200 he develops "Minkowskian geometry" and describes P("M") as the "inversive Minkowski plane". The Russian original of Yaglom's text was published in 1969. Between the two editions, Walter Benz (1973) published his book which included the homogeneous coordinates taken from "M".
Rotations in 4-dimensional Euclidean space
According to the German mathematician Felix Klein this formula was already known to Cayley in 1854.
Split-quaternion
In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name. Like the quaternions introduced by Hamilton in 1843, they form a four dimensional real vector space equipped with a multiplicative operation. Unlike the quaternion algebra, the split-quaternions contain nontrivial zero divisors, nilpotent elements, and idempotents. (For example, is an idempotent zero-divisor, and is nilpotent.) As a mathematical structure, they form an algebra over the real numbers, which is isomorphic to the algebra of 2 × 2 real matrices. For other names for split-quaternions see the Synonyms section below.
Bryan Allen (hang glider)
Bryan Lewis Allen (born October 13, 1952) is an American self-taught hang glider pilot and bicyclist. He achieved fame when he piloted (and provided the human power for) the two aircraft that won the first two Kremer prizes for human-powered flight, the "Gossamer Condor" (1977; the first human-powered aircraft to fly and meet specified criteria) and "Gossamer Albatross" (1979; the first human-powered aircraft to cross the English Channel). He later set world distance and duration records in a small pedal-powered blimp named "White Dwarf."
Magic square
The order four magic square Albrecht Dürer immortalized in his 1514 engraving "Melencolia I,", referred to above, is believed to be the first seen in European art. The square associated with Jupiter appears as a talisman used to drive away melancholy. It is very similar to Yang Hui's square, which was created in China about 250 years before Dürer's time. The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, and the corner squares (of the 4×4 as well as the four contained 3×3 grids). This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows (5+9+8+12 and 3+2+15+14), and in four kite or cross shaped quartets (3+5+11+15, 2+10+8+14, 3+9+7+15, and 2+6+12+14). The two numbers in the middle of the bottom row give the date of the engraving: 1514. The numbers 1 and 4 at either side of the date correspond respectively to the letters "A" and "D," which are the initials of the artist.
Axel jump
The Axel is a figure skating jump with a forward take off. It is named after Norwegian figure skater Axel Paulsen who, in 1882, was the first skater to perform the jump. Compared to other common figure skating jumps, an Axel has an extra ½ rotation in the air because of its forward take off. Most skaters perform the jump with counterclockwise rotation, taking off from the left forward outside edge and landing on the right back outside edge. The Axel can also be done as a double jump with 2½ rotations, or as a triple jump with 3½ rotations, or a quadruple Axel with 4½ rotations, but no skater has yet accomplished a quadruple Axel in competition.
Robert Bradshaw (figure skater)
Bradshaw was the first figure skater to successfully perform a double axel jump initiated and performed with the arms folded in competition. This variation of the Axel requires significant height to be able to complete the rotations, rather than the more common technique of performing a lower jump with very fast rotation generated by pulling the arms into the body.
Bivector
The bivector was first defined in 1844 by German mathematician Hermann Grassmann in exterior algebra as the result of the exterior product of two vectors. Just the previous year, in Ireland, William Rowan Hamilton had discovered quaternions. It was not until English mathematician William Kingdon Clifford in 1888 added the geometric product to Grassmann's algebra, incorporating the ideas of both Hamilton and Grassmann, and founded Clifford algebra, that the bivector as it is known today was fully understood.
Bodyboarding
El Rollo: Originally completed simultaneously by Hawaii's Pat Caldwell at Sandy Beach & Hawaii's Mike Stewart at Kona breaks such as Kahalu'u Bay.
Reverse Rollo: Originally completed by Kauai's Kyle Maligro. 
Invert: Unknown.
ARS (Air Roll Spin): Originally completed by Australia's Michael Eppelstun. Argued that California's Jacob Reeve completed it at the same time.
Backflip: Originally completed by Australia's Michael Eppelstun.
Double Rollo: Originally completed by Australia's Michael Eppelstun.
Air forward 360°: Originally completed by Hawaii's Mike Stewart.
Air reverse 360°: Originally completed by Hawaii's Mike Stewart.
Air Hubb (Forward air to el rollo): Originally completed by Kauai's Jeff Hubbard.
Gainer Flip: Originally completed by Tahiti's David Tuarau. 
GORF (Invert to front flip forward): Originally completed by Nathan "Nugget" Purcell.
Invert to Reverse 360° "Inverse": Originally completed by Kauai's Jeff Hubbard.
Devert (Invert to reverse el rollo): Originally completed by Kauai's David Phillips.
Air reverse 720°: Originally completed by Hawaii's Jeff Hubbard.
ATS - Aéreo Thiago Schmitd (Thiago Schmitd's Air): Originally completed by Brazil's Thiago SchmitdPhylis Dameron was the first person, man or woman, to ride big Waimea Bay on a bodyboard in the late 1970s. During the early 1990s in Brazil, Mariana Nogueira, Glenda Koslowski, and Stephanie Petterson set standards that pushed women's bodyboarding to a world class level. Stephanie Petterson won the first official World Championship of Women's Bodyboarding at Pipeline in 1990. It was the first women's event ever held there and initiated the longest running women's wave sport event in the world. 2009 marked the event's 20th anniversary.
Dual quaternion
and
then
Roy Lunn
As Jeep's chief engineer, Lunn orchestrated 4WD's next leap ahead when he joined the AMC Concord body with a reconstituted Jeep driveline. According to former AMC chairman, Gerald C. Meyers, "our initial reaction to Lunn's concoction was, 'What the hell is it?' The body was raised an extra four inches for transfer-case clearance and the wheel wells were wide open." This became the AMC Eagle, an integration and application of AMC and Jeep engineering technologies, which was America’s first four-wheel drive car.
Salchow jump
Timothy Goebel is recognized to have landed the first quadruple Salchow at the 1998 Junior Series Final. Goebel's jump, however, used the aforementioned controversial two-footed Salchow technique. The first female skater to have landed a quadruple Salchow in competition was Miki Ando at the 2002 Junior Grand Prix Final. Until 2018, no other female skater successfully landed the jump until Alexandra Trusova landed it at the 2018 World Junior Figure Skating Championships, at just age 13.
Kim Min-seok (figure skater)
Kim Min-seok (Korean: 김민석, born February 19, 1993) is a South Korean former figure skater. He is the 2012 Asian Trophy silver medalist, and a two-time (2009, 2010) South Korean national champion. He is the first Korean skater to land a triple axel in ISU competition.
Pair skating
The first throw triple axel jump performed in competition was by American pair team Rena Inoue and John Baldwin, Jr. at the 2006 U.S. Championships. They also performed it at the Four Continents Championships in 2006 and the 2006 Winter Olympics. The throw triple axel is a difficult throw to accomplish because the woman must perform 3 1/2 revolutions after being thrown by the man, a half-revolution more than other triple jumps, and because it requires a forward take-off.
Alexander McAulay
Alexander McAulay (9 December 1863 – 6 July 1931) was the first professor of mathematics and physics at the University of Tasmania, Hobart, Tasmania. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions".
Matt Chojnacki
In 1999, at Steamboat Springs, Colorado, Chojnacki became the first person to land a quadruple somersault (four back flips with two twists) on snow with a clean (no touch) landing. That same season, along with Eric Bergoust and Nicolas Fontaine, Chojnacki tied the World Record for aerial skiing by completing a triple twisting quadruple somersault, a 17-year-old record set by Frank Bare, Jr. in 1983. Then on April 4, 2001, at Winter Park resort, Colorado, Chojnacki broke that mark by adding a full twist to the quad for a Half-Rudy (one and one-half)-Full-Full, or a quadruple back somersault with four twists and the current Guinness World Record. Chojnacki was partially trained and coached by Frank Bare, Jr. for that jump. In addition, he set the aerials water ramps world record in 2000, at the Utah Olympic Park, by completing a quintuple twisting quadruple back somersault with a Half-Rudy (one and one-half)-DoubleFull-Full.
Quadrilateralized spherical cube
In mapmaking, a quadrilateralized spherical cube, or quad sphere for short, is an equal-area mapping and binning scheme for data collected on a spherical surface (either that of the Earth or the celestial sphere). It was first proposed in 1975 by Chan and O'Neill for the Naval Environmental Prediction Research Facility.
Zhang Min (figure skater)
At the 1999 Four Continents, Zhang became the first skater to land a clean quadruple toe loop in the short program at an ISU Championship. He has also landed quadruple salchows in competition. He is the second person to land three quadruple jumps in one program. At the 2006 World Championships, the day before his 30th birthday, he landed a 4T-3T combination and 4S in his free skate. He named Elvis Stojko as his idol in the sport.
Gordon McKellen
Although other skaters had practiced triple axels before then, McKellen was the first skater to attempt them in public performances. He landed several in exhibition in 1974–1975, as King of the Lake Placid Winter Festival exhibition and during the exhibitions following his third National championship win in Providence. The triple axel was not landed in competition until Vern Taylor did it in 1978.
Rotation formalisms in three dimensions
Given the Euler axis and angle , the quaternion
Ludmila Nelidina
Nelidina landed a triple axel in competition at the 2002 Skate America. Together with Yukari Nakano, who also completed a triple axel at that competition, Nelidina was the first female skater in 10 years to perform a triple axel in international competition. She is the first European lady skater to land a triple axel in competition, the other skaters having been from Japan and the United States.
Parameshvara
He was the first mathematician to give the radius of circle with an inscribed quadrilateral. The expression is sometimes attributed to Lhuilier (1782), 350 years later. With the sides of the cyclic quadrilateral being "a, b, c," and "d", the radius "R" of the circumscribed circle is:
Patti Gustafson
Gustafson and Kollen were the first pair team to perform the throw axel, which was invented by their coach Ronald Ludington.
Torstein Horgmo
At the Winter X Games Aspen in January 2013, Horgmo was the first person ever to land a switch backside triple cork 1440 in competition, earning him a perfect score of 50/50 for the second year in a row and the gold medal in Big Air. In competitions following Horgmo was able to win slopestyle gold and silver in the Burton European and US Opens respectively. In the Burton US Open, Horgmo was the only rider to land a triple cork on the slopestyle course, but lost to Shredbots teammate Mark McMorris by a narrow margin.
Double Eagle (balloon)
Double Eagle was a helium balloon piloted by Ben Abruzzo and Maxie Anderson in a failed attempt to cross the Atlantic Ocean in 1977. It was the eleventh recorded attempt to make the crossing, which had been an open challenge in ballooning for more than a century. The balloon launched from Marshfield, Massachusetts on September 9. After being blown off course by stormy weather, the team was forced to ditch three miles off the coast of Iceland on September 12, 65½ hours after taking off. Abruzzo and Anderson, along with Larry Newman, went on to complete the first successful Atlantic crossing the following year aboard "Double Eagle II".
Loop jump
The loop can also be done as a double, triple, or quadruple, with two, three, or four rotations, respectively. Dick Button performed the first triple loop jump at the 1952 Winter Olympics. The first female skater known to be able to perform a triple loop was Gaby Seyfert in 1968. Yuzuru Hanyu (JPN) became the first skater in history to successfully land a quadruple loop in competition at the 2016 Autumn Classic International.
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors.
Oxia Palus quadrangle
Mars Pathfinder landed in the Oxia Palus quadrangle at , on July 4, 1997. Crater names in Oxia Palus are a Who's Who for famous scientists. Besides Galilei and da Vinci, some of the people who discovered the atom and radiation are honored there: Curie, Becquerel, and Rutherford.
Vitali Egorov
Egorov was one of the first skaters in the world to land a triple Axel jump, performing it in April 1981, at the USSR Cup competition in Sverdlovsk, where he won the bronze medal. In March 1982, he won the 5th USSR Winter Spartakiada. He is a coach in Kharkiv.
Charles Rigoulot
As a weightlifter he won the gold medal in the 82.5 kg division at the 1924 Summer Olympics. Between 1923 and 1926 he set eight official world records. In 1924, he became the first person to clean and jerk more than 400 pounds, using the non-revolving barbells of that time. In 1930, he became the first person to complete an overhead lift of the Apollon Railway Car Wheels, an awkwardly-shaped 166 kg (366 lb) barbell-shaped set of train wheels used by the stage strongman Louis Uni, and the predecessor of "Apollon's Axle".
Quaternions and spatial rotation
The three rotation axes A, B, and C form a spherical triangle and the dihedral angles between the planes formed by the sides of this triangle are defined by the rotation angles. Hamilton presented the component form of these equations showing that the quaternion product computes the third vertex of a spherical triangle from two given vertices and their associated arc-lengths, which is also defines an algebra for points in Elliptic geometry.
Double (basketball)
A quadruple-double is defined as a performance in which a player accumulates a double digit number total in four of five statistical categories—points, rebounds, assists, steals and blocked shots—in a game. This feat is extremely rare: only four players have officially recorded a quadruple-double in National Basketball Association (NBA) history. The first American male player above the high school level to officially record a quadruple-double was Nate Thurmond, who achieved this feat in 1974 while playing for the NBA's Chicago Bulls. The first American female player above the high school level to officially record a quadruple-double was Ann Meyers, who achieved this feat in 1978 while playing for the UCLA Bruins, when women's college sports were under the auspices of the AIAW. The first male player in NCAA Division I history to record a quadruple-double was Lester Hudson in 2007. The first Division I women's player to have officially recorded a quadruple-double since the NCAA began sponsoring women's sports in 1981–82 was Veronica Pettry of Loyola–Chicago in 1989. Only three other women have done so since, and Shakyla Hill's quadruple-double for Grambling State in 2018 was the first since 1993. An earlier player, Jackie Spencer of Louisville, accomplished the feat against Cincinnati during the 1984–85 season, but the NCAA did not record assists and steals throughout Division I women's basketball at that time. The Metro Conference, then home to both schools, did officially record these statistics, but the NCAA did not start doing so until 1985–86 for assists and 1987–88 for steals.
Frederick Walker Baldwin
Baldwin used his engineering skills to help build the "Silver Dart" plus several other experimental aircraft. On March 12, 1908 at Lake Keuka, New York he became the first Canadian, and either the third or fourth North American, to pilot an airplane. William Whitney Christmas claimed to have first flown his aircraft on various dates from September 1907 to March 1908 near Fairfax, Virginia. The first two successful pilots were, of course, the famous Wright brothers, but it seems unlikely that it will ever be firmly established whether Christmas or Baldwin was the so-called "Third Man."
Winkel tripel projection
The Winkel tripel projection (Winkel III), a modified azimuthal map projection of the world, is one of three projections proposed by German cartographer Oswald Winkel (7 January 1874 – 18 July 1953) in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name "Tripel" (German for "triple") refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance.
Quadratrix of Hippias
The quadratrix is mentioned in the works of Proclus (412–485), Pappus of Alexandria (3rd and 4th centuries) and Iamblichus (c. 240 – c. 325). Proclus names Hippias as the inventor of a curve called quadratrix and describes somewhere else how Hippias has applied the curve on the trisection problem. Pappus only mentions how a curve named quadratrix was used by Dinostratus, Nicomedes and others to square the circle. He neither mentions Hippias nor attributes the invention of the quadratrix to a particular person. Iamblichus just writes in a single line, that a curve called a quadratrix was used by Nicomedes to square the circle.
Sikorsky Russky Vityaz
The Sikorsky Russky Vityaz (), or Russian Knight, previously known as the Bolshoi Baltisky () "(The Great Baltic)" in its first four-engined version, was the first four-engine aircraft in the world, designed by Igor Sikorsky and built at the Russian Baltic Railroad Car Works ("Russo-Baltiiskyi Vagonnyi Zavod" or "R-BVZ") in Saint Petersburg in early 1913.
Bjørn G. Andersen
At the University of Bergen, Andersen played a central role in building up the study of Quaternary geology. His students and the university benefited from his international contacts and he conducted filed trips to the Antarctic, South America and New Zealand. Most of all his contribution was to reveal the foundation of Scandinavian landscapes.
Andersen's first expedition to the South Pole came in a period of small Norwegian interest in the Antarctic after the great achievements of Roald Amundsen in 1911–1912. Andersen was the second Norwegian to visit the Pole after the Amundsen expedition. An American expedition which reached the Pole a week before him honored his achievements by naming a mountain escarpment Andersen Escarpment after him.
Frédéric Dambier
Frédéric Dambier (born 26 December 1977) is a French figure skater. He is a four-time French national silver medalist and competed at two Olympic Games. He twice placed fourth at the European Figure Skating Championships. He is the first French skater to land a quadruple salchow in competition.
Edward Turner
By now, living at various addresses in Peckham and East Dulwich, in the London Borough of Southwark and running Chepstow Motors, a Peckham Road motorcycle shop with a Velocette agency, Turner conceived the Square Four engine in 1928. At this time he was looking for work, showing drawings of his engine design to motorcycle manufacturers. The engine was essentially a pair of 'across frame' OHC parallel twins joined by their geared central flywheels, with a one-piece four-cylinder block (or Monobloc) and single head. The idea for the engine was rejected by BSA, but adopted by Ariel. Thus it became the Ariel Square Four, and not the BSA Square Four. Turner was then invited by Jack Sangster to join Ariel.
Poul la Cour
Telegraphy, the most important technological prerequisite for modern meteorology, soon became his main interest. In June 1874, the year in which Edison invented his quadruplex telegraphy, la Cour invented a telegraphic device based on tuning forks. The idea was to permit a number of telegraphers to send messages on a single wire, each using his own frequency. By using the resonance phenomenon of tuning forks it was possible to split out the messages at the receiving end of the wire. He patented his invention in London on 2 September 1874, but in the United States Alexander Graham Bell, Elisha Gray and others had been working along similar lines, which resulted in protests against his American patent applications. Having too little money to pay lawyers, he gave up his claim in America, and this invention was credited to Elisha Gray. La Cour however maintained that Gray had been working on the invention of the telephone, and only had changed his invention at the instant la Cour's American application was published. He could not help feeling some malicious pleasure when Graham Bell was awarded the telephone patent by applying only a few hours before Gray – as he later wrote in an autobiographical article.
Yuzuru Hanyu
Hanyu competed at the Autumn Classic International, where he won the gold medal and became the first skater in history to successfully land a quadruple Loop in competition.
Pappus of Alexandria
Of Book IV the title and preface have been lost, so that the program has to be gathered from the book itself. At the beginning is the well-known generalization of Euclid I.47 (Pappus's area theorem), then follow various theorems on the circle, leading up to the problem of the construction of a circle which shall circumscribe three given circles, touching each other two and two. This and several other propositions on contact, e.g. cases of circles touching one another and inscribed in the figure made of three semicircles and known as arbelos ("shoemakers knife") form the first division of the book; Pappus turns then to a consideration of certain properties of Archimedes's spiral, the conchoid of Nicomedes (already mentioned in Book I as supplying a method of doubling the cube), and the curve discovered most probably by Hippias of Elis about 420 BC, and known by the name, τετραγωνισμός, or quadratrix. Proposition 30 describes the construction of a curve of double curvature called by Pappus the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time. The area of the surface included between this curve and its base is found – the first known instance of a quadrature of a curved surface. The rest of the book treats of the trisection of an angle, and the solution of more general problems of the same kind by means of the quadratrix and spiral. In one solution of the former problem is the first recorded use of the property of a conic (a hyperbola) with reference to the focus and directrix.
1948 Winter Olympics
Eighteen-year-old American Dick Button completed the unprecedented North American sweep of the figure skating gold medals. He led the field after the compulsory skate and then won the gold medal by becoming the first person to ever complete a double axel in competition. Later in the 1952 Olympics, Dick Button would win gold a second time. His victory came at the expense of Swiss world champion Hans Gerschwiler who fell during the free skate. Despite the mishap Gershwiler would win the silver medal.
Alain Colas
Alain Colas (16 September 1943 – 16 November 1978)) was a French sailor, the first to complete a solitary round-the-world race in a multihull. He met Éric Tabarly in Sydney in 1967, and bought Pen Duick IV from him in 1970, and won the "Transat" in 1972. In 1972, he started the construction of a 72m (236 feet) 4 masted monohull for the 1976 "Transat". He broke his right ankle, underwent 22 surgeries, and got back on his feet for the solitary transatlantic race. Éric Tabarly won, and Alain Colas arrived 2nd but was classed 5th. On 5 November 1978, he took part in his last race, the first Route du Rhum. On 16 November 1978, as he passed the Azores, he sent his last radio message saying that everything was alright and sailing well. Neither his boat "Manureva" nor his body were ever found.
Alvin Kraenzlein
Alvin Christian "Al" Kraenzlein (December 12, 1876 – January 6, 1928), known as "the father of the modern hurdling technique", was an American track-and-field athlete, and the first sportsman in the history of Olympic games to win four individual gold medals in a single discipline at the 1900 Summer Olympics in Paris. Before, Carl Schuhmann, a German athlete, won four Olympic titles in gymnastics and wrestling at the 1896 Summer Olympics in Athens. , Alvin Kraenzlein is the only track-and-field athlete who has won four individual titles at one Olympics. Kraenzlein is also known for developing a pioneering technique of straight-leg hurdling, which allowed him to set two world hurdle records. He is an Olympic Hall of Fame (1984) and USA Track & Field (1974) inductee.
Versor
This versor was used by Homersham Cox (1882/83) in relation to quaternion multiplication. The primary exponent of hyperbolic versors was Alexander Macfarlane as he worked to shape quaternion theory to serve physical science. He saw the modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend the concept to 4-space. Problems in that algebra led to use of biquaternions after 1900. In a widely circulated review of 1899, Macfarlane said:
Today the concept of a one-parameter group subsumes the concepts of versor and hyperbolic versor as the terminology of Sophus Lie has replaced that of Hamilton and Macfarlane.
In particular, for each ' such that or , the mapping formula_14 takes the real line to a group of hyperbolic or ordinary versors. In the ordinary case, when ' and − are antipodes on a sphere, the one-parameter groups have the same points but are oppositely directed. In physics, this aspect of rotational symmetry is termed a doublet.
2002 Skate America
Yukari Nakano and Ludmila Nelidina both landed a triple axel in their free skating, together becoming the first female skaters to perform the jump in international competition since Midori Ito landed it at the 1992 Winter Olympics. Nakano landed it first and Nelidina, who skated after her, also performed it successfully.
Vern Taylor
Vern Taylor is a Canadian figure skater and coach. He is the 1978 and 1979 Canadian silver medalist and 1977 bronze medalist. At the 1978 World Figure Skating Championships, he became the first person to land a triple axel jump in competition.
Alfredo Codona
Alfredo Codona (October 7, 1893 – July 30, 1937) was an Italian American trapeze artist who was a member of the world-famous "Flying Codonas" and was the first aerialist to continually perform the triple somersault. Alfredo came from an itinerant performing family who emigrated from Italy in the 1790s to the UK, where Alfredo's grandfather Henry (Enrico) Codona was born. The original Codoni or Cardoni family name evolved in the early to mid 1800s into the name Codona, which is widely recognised in punch and judy, circus and of fairground folklore - Codona is practically a household name in the entertainment business in Scotland where the family owns a large static fairground site in Aberdeen and other members of the family travel around the country with portable amusement rides.
Three Poles Challenge
The first person to reach all three locations was Edmund Hillary. He reached the top of Everest in May 1953, the South Pole in January 1958 and made it to the North Pole in company with Neil Armstrong in April 1985.
Hillary flew to the North Pole. The first person to reach all three locations on foot was Erling Kagge. He had reached all three by May 1994, being 6 months faster than the next person. On 5 August 1997 Antoine de Choudens (France, 1969–2009) became the only climber to accomplish the Three Poles Challenge on foot without using supplementary oxygen on the Everest climb. Tina Sjögren became the first woman to complete the challenge in 2002.
Quadruple jump controversy
Jeffrey Buttle's win at the 2008 Worlds officially disproved the already long-standing notion that a quad was needed to win the big titles. His win is credited to have been the spark that ignited the quad controversy that came to a head at the Vancouver Olympic Games. Brian Joubert, the first European skater to land three quads in a program, expressed his strong disappointment over the results and stated that the value of the jump should be raised in the current scoring system. Evan Lysacek, like Joubert, commented that a quad was an essential part of men's skating. In 2009, Lysacek became the second consecutive figure skater to win the world championship without a quadruple jump.
Ashley Caldwell
Caldwell then suffered from back to back ACL tears, missing the 2012 and 2013 competitive seasons. Upon returning she claimed the silver medal at her first world cup event in China earning a spot to the Sochi Olympics. She placed 10th place after a bad landing on her first finals jump. She competed again in Beijing in December 2014 winning gold, alongside her 19-year-old teammate Kiley McKinnon, who won silver. She became the first female skier to land a quadruple twisting triple back flip at the 2017 World Championship in Sierra Nevada, Spain. Caldwell won the event alongside teammate Jon Lillis.
Dick Button
Button is credited as having been the first skater to successfully land the double axel jump in competition in 1948, as well as the first triple jump of any kind – a triple loop – in 1952. He also invented the flying camel spin, which was originally known as the "Button camel".
Jean-Baptiste Singelée
As a longtime friend of Adolphe Sax, the inventor of the saxophone (they met as students at the Royal School of Music), he encouraged Sax to develop the four principal members of the saxophone family, and composed what is very likely the first work ever written for the saxophone quartet, his "Premier Quatuor", Op. 53, completed in 1857. In addition to his saxophone works, Singelée is credited with composing 12 concertos, many solo works for violin and other instruments as well as music for ballet.
Flexagon
The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone, who was studying at Princeton University in the United States in 1939. His new American paper would not fit in his English binder so he cut off the ends of the paper and began folding them into different shapes. One of these formed a trihexaflexagon. Stone's colleagues Bryant Tuckerman, Richard Feynman, and John Tukey became interested in the idea and formed the Princeton Flexagon Committee. Tuckerman worked out a topological method, called the Tuckerman traverse, for revealing all the faces of a flexagon.
Pterodactylus
It was the German/French scientist Johann Hermann who first stated that "Pterodactylus" used its long fourth finger to support a wing membrane. In March 1800, Hermann alerted the French scientist George Cuvier to the existence of Collini's fossil, believing that it had been captured by the occupying armies of Napoleon and sent to the French collections in Paris (and perhaps to Cuvier himself) as war booty; at the time special French political commissars systematically seized art treasures and objects of scientific interest. Hermann sent Cuvier a letter containing his own interpretation of the specimen (though he had not examined it personally), which he believed to be a mammal, including the first known life restoration of a pterosaur. Hermann restored the animal with wing membranes extending from the long fourth finger to the ankle and a covering of fur (neither wing membranes nor fur had been preserved in the specimen). Hermann also added a membrane between the neck and wrist, as is the condition in bats. Cuvier agreed with this interpretation, and at Hermann's suggestion, Cuvier became the first to publish these ideas in December 1800 in a very short description. Cuvier remarked, "[It is not possible to doubt that the long finger served to support a membrane that, by lengthening the anterior extremity of this animal, formed a good wing.]" However, contrary to Hermann, Cuvier was convinced the animal was a reptile.
Midori Ito
During the peak of her career, Ito performed much the same jump content as the top male skaters of the time. She was the first ladies' skater to perform a triple-triple jump combination and the first to perform the triple axel. In March 1990, Jill Trenary said, "I was in awe of how high she jumps." In 1990, Scott Hamilton said "it will be 50 years before we see anything like Midori Ito again," and Toller Cranston, the same year, noted that "she is beyond 6.0."
Split-quaternion
The coquaternions were initially introduced (under that name) in 1849 by James Cockle in the London–Edinburgh–Dublin Philosophical Magazine. The introductory papers by Cockle were recalled in the 1904 "Bibliography" of the Quaternion Society. Alexander Macfarlane called the structure of coquaternion vectors an "exspherical system" when he was speaking at the International Congress of Mathematicians in Paris in 1900.
Vincent Restencourt
Restencourt started to skate at the age of 6, having been introduced to the activity by his sister, who also competed in figure skating. He represented the Champigny club and was coached by André Brunet. He was the first French skater to land a quadruple jump, a toe loop, in competition.
Angle modulation
The combination of phase modulation with amplitude modulation, practiced as early as 1874 by Thomas Edison in the quadruplex telegraph for transmitting four signals, two each in both directions of transmission, constitutes the polar modulation technique.
History of quaternions
In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.
History of algebra
Arabic mathematicians treated irrational numbers as algebraic objects. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. He was also the first to solve three non-linear simultaneous equations with three unknown variables.
Nathan Chen
In January 2016, Chen made history at the U.S. Championships by becoming the first American man to land two quadruple jumps in the short program. On January 24, he became the first man in the world to land four quadruple jumps in a long program. He finished third overall behind Adam Rippon and Max Aaron, who landed zero and two quads, respectively, reigniting the debate over whether artistry should trump athleticism in figure skating scoring. While attempting a jump during exhibitions on the same day, Chen sustained an avulsion injury to his left hip, leading to surgery on January 27.
Kurt Browning
On March 25, 1988, at the 1988 World Championships in Budapest, Hungary, Browning landed the first ratified quadruple jump (a toe loop) in competition. This accomplishment is listed in the Guinness Book of Records. Jozef Sabovčík had previously landed a quad toe loop at the 1986 European Championships which was recognized at the event but then ruled invalid three weeks later. Browning later said, "I remember that there were a few people landing the jump (in practice) long before I did, and by watching them I was inspired to try it myself. After landing it, I certainly expected more skaters to start doing it in competition. I was surprised in the next few years when that really did not happen." Browning is also known for his intricate, fast, often lighthearted footwork.
Hyperbolic quaternion
It was Alexander Macfarlane who promoted this concept in the 1890s as his "Algebra of Physics", first through the American Association for the Advancement of Science in 1891, then through his 1894 book of five "Papers in Space Analysis", and in a series of lectures at Lehigh University in 1900.
Lutz jump
Today the Lutz is often done in double or triple versions. Alena Vrzáňová of Czechoslovakia was the first woman credited with a double Lutz, performed at the 1949 World Championships. Donald Jackson of Canada was the first skater to execute a triple Lutz jump in competition, at the 1962 World Championships; Denise Biellmann of Switzerland is credited as the first woman to do so, at the 1978 European Championships. Brandon Mroz of the United States is credited with landing the first quadruple Lutz jump in a sanctioned competition at the 2011 Colorado Springs Invitational, a club competition sanctioned by U.S. Figure Skating; Mroz's jump was subsequently ratified by the International Skating Union after video review. On November 12, Mroz landed it in the short program at 2011 NHK Trophy, becoming the first skater to land it in an international competition. On November 2015 Jin Boyang became the first man to land the quad lutz with a positive GOE at an international competition and a quad lutz triple toe. On November 25, 2017 Nathan Chen became the first man to land two quadruple Lutz jumps in competition during the free skating portion of the Skate America Grand Prix Competition. On February 17, 2018, Vincent Zhou became the first to land a Quad Lutz at any Winter Olympic Competition. On October 12, 2018, Alexandra Trusova became the first female skater to land a Quad Lutz at the 2018 JGP Armenia.
Brian Orser
Orser became the second man to land the triple Axel when he performed it in winning his Canadian junior title in 1979, at a time when few senior skaters were even attempting it. Over the next few years, Orser performed the jump more frequently and more consistently than any other skater of the time. Orser became the first man to land the triple axel at the Olympics when he landed it in his free skate at the 1984 Winter Olympics. He won the silver medal behind Scott Hamilton, and then won the silver at 1984 Worlds, again behind Hamilton. Only Orser's low placements in the compulsory figures prevented him from winning both titles.
Archimedes' quadruplets
In geometry, Archimedes' quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making them Archimedean circles.
Aerodynamics
In 1799, Sir George Cayley became the first person to identify the four aerodynamic forces of flight (weight, lift, drag, and thrust), as well as the relationships between them, and in doing so outlined the path toward achieving heavier-than-air flight for the next century. In 1871, Francis Herbert Wenham constructed the first wind tunnel, allowing precise measurements of aerodynamic forces. Drag theories were developed by Jean le Rond d'Alembert, Gustav Kirchhoff, and Lord Rayleigh. In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight. Otto Lilienthal, the first person to become highly successful with glider flights, was also the first to propose thin, curved airfoils that would produce high lift and low drag. Building on these developments as well as research carried out in their own wind tunnel, the Wright brothers flew the first powered airplane on December 17, 1903.
Brian Joubert
Joubert was considered a strong jumper during his competitive career. He landed the quadruple salchow jump in competition and had a consistent quadruple toe loop jump. In 2013, he became the first skater to land 100 quadruple jumps in international competition. At the 2006 Cup of Russia competition, Joubert landed three quadruple jumps in his free skate: two toe loops (one in combination) and a Salchow, the first skater to accomplish this under the IJS. Joubert has stated in interviews that he considers quadruple jumps to be important for the future of figure skating as a sport. Although the triple lutz was normally consistent for him in practice, he twice cut his right foot while picking in for the jump.
Timothy Goebel
Timothy Richard Goebel (born September 10, 1980) is an American former competitive figure skater. He is the 2002 Olympic bronze medalist. He was the first person to land a quadruple salchow jump in competition and the first person to land three quadruple jumps in one program. He landed 76 career quadruple jumps before his retirement in 2006.
Foundations of mathematics
For the first time, the limits of mathematics were explored. Niels Henrik Abel (1802–1829), a Norwegian, and Évariste Galois, (1811–1832) a Frenchman, investigated the solutions of various polynomial equations, and proved that there is no general algebraic solution to equations of degree greater than four (Abel–Ruffini theorem). With these concepts, Pierre Wantzel (1837) proved that straightedge and compass alone cannot trisect an arbitrary angle nor double a cube. In 1882, Lindemann building on the work of Hermite showed that a straightedge and compass quadrature of the circle (construction of a square equal in area to a given circle) was also impossible by proving that  is a transcendental number. Mathematicians had attempted to solve all of these problems in vain since the time of the ancient Greeks.
Quadruplex telegraph
The technology was invented by American inventor Thomas Edison, who sold the rights to Western Union in 1874 for the sum of $10,000.
Axial engine
Heraclio Alfaro was a Spanish aviator who was knighted at the age of 18 by King Alfonso XIII of Spain for designing, building, and flying Spain's first airplane. He developed a barrel engine for aircraft use which was later produced by the Indian Motocycle Manufacturing Company as the "Alfaro". It was a perfect example of the "put in everything" design, as it included a sleeve valve system based on a rotating cylinder head, a design that never entered production on any engine. It was later developed further for use in the Doman helicopter by Stephen duPont, son of the president of the Indian Motorcycle Company, who had been one of Alfaro's students at Massachusetts Institute of Technology.
Delta wing
Triangular stabilizing fins for rockets were described as early as 1529-1556 by Conrad Haas and in the 17th century by Kazimierz Siemienowicz. A true lifting wing in delta form did not appear until 1867, when it was patented by J.W. Butler and E. Edwards in a design for a dart-shaped rocket-propelled aeroplane. This was followed by other proposals, such as a biplane version by Butler and Edwards, and a jet-propelled version by the Russian Nicholas de Telescheff.