Portal:Mathematics
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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 owner Matthew Benham influenced both Brentford FC in the UK and FC Midtjylland in Denmark to use mathematical modelling to recruit undervalued football players?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
- ... that mathematician Daniel Larsen was the youngest contributor to the New York Times crossword puzzle?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that the prologue to The Polymath was written by Martin Kemp, a leading expert on Leonardo da Vinci?
- ... that ten-sided gaming dice have kite-shaped faces?
- ... that people in Madagascar perform algebra on tree seeds in order to tell the future?
- ... that the mathematical infinity symbol ∞ may be derived from the Roman numerals for 1000 or for 100 million?
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- ...that the Rule 184 cellular automaton can simultaneously model the behavior of cars moving in traffic, the accumulation of particles on a surface, and particle-antiparticle annihilation reactions?
- ...that a cyclic cellular automaton is a system of simple mathematical rules that can generate complex patterns mixing random chaos, blocks of color, and spirals?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that the axiom of choice is logically independent of the other axioms of Zermelo–Fraenkel set theory?
- ...that the Pythagorean Theorem generalizes to any three similar shapes on the three sides of a right-angled triangle?
- ...that the orthocenter, circumcenter, centroid and the centre of the nine-point circle all lie on one line, the Euler line?
- ...that an arbitrary quadrilateral will tessellate?
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A polar grid with several angles labeled Image credit: User:Mets501 |
The polar coordinate system is a two-dimensional coordinate system in which points are given by an angle and a distance from a central point known as the pole (equivalent to the origin in the more familiar Cartesian coordinate system). The polar coordinate system is used in many fields, including mathematics, physics, engineering, navigation and robotics. It is especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; in the Cartesian coordinate system, such a relationship can only be found through trigonometric formulae. For many types of curves, a polar equation is the simplest means of representation of variables.
It is known that the Greeks used the concepts of angle and radius. The astronomer Hipparchus (190-120 BC) tabulated a table of chord functions giving the length of the chord for each angle, and there are references to his using polar coordinates in establishing stellar positions. (Full article...)
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