Portal:Mathematics
The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that more than 60 scientific papers authored by mathematician Paul Erdős were published posthumously?
- ... that multiple mathematics competitions have made use of Sophie Germain's identity?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that Fairleigh Dickinson's upset victory over Purdue was the biggest upset in terms of point spread in NCAA tournament history, with Purdue being a 23+1⁄2-point favorite?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that the British National Hospital Service Reserve trained volunteers to carry out first aid in the aftermath of a nuclear or chemical attack?
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- ... that economists blame market failures on non-convexity?
- ... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people?
- ... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks?
- ... that the Herschel graph is the smallest possible polyhedral graph that does not have a Hamiltonian cycle?
- ... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die?
- ... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree?
- ... that the Hadwiger conjecture implies that the external surface of any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient?
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Johannes Kepler Image credit: User:ArtMechanic |
Johannes Kepler (1571 – 1630) was an Austrian Lutheran mathematician, astronomer and a key figure in the 17th century astronomical revolution. He is best known for his laws of planetary motion, based on his works Astronomia nova and Harmonice Mundi; Kepler's laws provided one of the foundations of Isaac Newton's theory of universal gravitation. Before Kepler, planets' paths were computed by combinations of the circular motions of the celestial orbs; after Kepler astronomers shifted their attention from orbs to orbits—paths that could be represented mathematically as an ellipse.
During his career Kepler was a mathematics teacher at a Graz seminary school (later the University of Graz, Austria), an assistant to Tycho Brahe, court mathematician to Emperor Rudolf II, mathematics teacher in Linz, Austria, and adviser to General Wallenstein. He also did fundamental work in the field of optics and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei.
Kepler lived in an era when there was no clear distinction between astronomy and astrology, while there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of the more prestigious discipline of philosophy). (Full article...)
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