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 Donn Piatt threw his mathematics teacher out of the window?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that multiple mathematics competitions have made use of Sophie Germain's identity?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that Ukrainian baritone Danylo Matviienko, who holds a master's degree in mathematics, appeared as Demetrius in Britten's opera A Midsummer Night's Dream at the Oper Frankfurt?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
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- … that the best known lower bound for the length of the smallest superpermutation was first posted anonymously to the internet imageboard 4chan?
- ...that the mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?
- ...that a regular heptagon is the regular polygon with the fewest sides which is not constructible with a compass and straightedge?
- ...that the regular trigonometric functions and the hyperbolic trigonometric functions can be related without using complex numbers through the Gudermannian function?
- ...that the Catalan numbers solve a number of problems in combinatorics such as the number of ways to completely parenthesize an algebraic expression with n+1 factors?
- ...that a ball can be cut up and reassembled into two balls, each the same size as the original (Banach-Tarski paradox)?
- ...that it is impossible to devise a single formula involving only polynomials and radicals for solving an arbitrary quintic equation?
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Example of a four color map Image credit: User:Inductiveload |
The four color theorem states that given any plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent if they share a border segment, not just a point. "Color by Number" worksheets and exercises, which combine learning art and math for people of young ages, are a good example of the four color theorem.
It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (even though with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.
The four color theorem was the first major theorem to be proven using a computer, and the proof is disputed by some mathematicians because it would be infeasible for a human to verify by hand (see computer-aided proof). Ultimately, in order to believe the proof, one has to have faith in the correctness of the compiler and hardware executing the program used for the proof.
The lack of mathematical elegance was another factor, and to paraphrase comments of the time, "a good mathematical proof is like a poem — this is a telephone directory!" (Full article...)
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