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 in the aftermath of the American Civil War, the only Black-led organization providing teachers to formerly enslaved people was the African Civilization Society?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that circle packings in the form of a Doyle spiral were used to model plant growth long before their mathematical investigation by Doyle?
- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
- ... 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 after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
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- ...that the set of rational numbers is equal in size to the set of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
- ...that it is unknown whether π and e are algebraically independent?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that it is possible for a three-dimensional figure to have a finite volume but infinite surface area, such as Gabriel's Horn?
- ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
- ...that the primality of a number can be determined using only a single division using Wilson's Theorem?
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The four charts each map part of the circle to an open interval, and together cover the whole circle. Image credit: User:KSmrq |
A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension is important. For example, lines are one-dimensional, and planes two-dimensional.
In a one-dimensional manifold (or one-manifold), every point has a neighborhood that looks like a segment of a line. Examples of one-manifolds include a line, a circle, and two separate circles. In a two-manifold, every point has a neighborhood that looks like a disk. Examples include a plane, the surface of a sphere, and the surface of a torus.
Manifolds are important objects in mathematics and physics because they allow more complicated structures to be expressed and understood in terms of the relatively well-understood properties of simpler spaces. (Full article...)
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