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. Used for calculation, it is considered the most important subject. 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 pi can be computed using only the number 2 by the work of Viète?
- … that the Riemann Hypothesis, one of the Millennium Problems, depends on the asymptotic growth of the Mertens Function?
- … that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater?
- … 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?
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- ... that West Virginia State College professor Angie Turner King was an educator and mentor to entomologist Margaret S. Collins and NASA mathematician Katherine Johnson of Hidden Figures?
- ... that when Ruth Stokes defended her dissertation on the theory of linear programming in 1931, she became the first person to earn a doctorate in mathematics from Duke University?
- ... that former math teacher Dominic Gates won a Pulitzer Prize for his aerospace reporting?
- ... that a mathematical conjecture about tiling space by cubes was transformed into a problem in graph theory that became a benchmark for clique-finding algorithms?
- ... that the fall of the Berlin Wall was the result of a bureaucratic mistake?
- ... that William Chapple discovered Euler's theorem and Poncelet's porism?
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All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Image credit: User:Tttrung |
The trigonometric functions are functions of an angle; they are most important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers.
The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by ancient Greek, Indian and Arab mathematicians. (Full article...)
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