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 the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that after Florida schools banned 54 mathematics books, Chaz Stevens petitioned that they also ban the Bible?
- ... that subgroup distortion theory, introduced by Misha Gromov in 1993, can help encode text?
- ... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that the British National Hospital Service Reserve trained volunteers to carry out first aid in the aftermath of a nuclear or chemical attack?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
More did you know –
- ...the Piphilology record (memorizing digits of Pi) is 70000 as of Mar 2015?
- ...that people are significantly slower to identify the parity of zero than other whole numbers, regardless of age, language spoken, or whether the symbol or word for zero is used?
- ...that Auction theory was successfully used in 1994 to sell FCC airwave spectrum, in a financial application of game theory?
- ...properties of Pascal's triangle have application in many fields of mathematics including combinatorics, algebra, calculus and geometry?
- ...work in artificial intelligence makes use of swarm intelligence, which has foundations in the behavioral examples found in nature of ants, birds, bees, and fish among others?
- ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
- ...that modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?
Selected article –
3D illustration of a stereographic projection from the north pole onto a plane below the sphere. Image credit: Mark Howison |
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.
Intuitively, then, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography, geology, and photography. (Full article...)
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