Portal:Mathematics

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The Mathematics Portal

Mathematics, from the Greek: μαθηματικά or mathēmatiká, is the study of patterns. Such patterns include quantities (numbers) and their operations, interrelations, combinations and abstractions; and of space configurations and their structure, measurement, transformations, and generalizations. Mathematics evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, shapes and motions of abstract objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.

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	A Platonic solid is a convex regular polyhedron. These are the three-dimensional analogs of the convex regular polygons. There are precisely five such figures (shown on the left). The name of each figure is derived from the number of its faces: respectively 4, 6, 8, 12 and 20. They are unique in that the sides, edges and angles are all congruent. Due to their aesthetic beauty and symmetry, the Platonic solids have been a favorite subject of geometers for thousands of years. They are named after the ancient Greek philosopher Plato who claimed the classical elements were constructed from the regular solids. The Platonic solids have been known since antiquity. The five solids were certainly known to the ancient Greeks and there is evidence that these figures were known long before then. The neolithic people of Scotland constructed stone models of all five solids at least 1000 years before Plato.
Tetrahedron

Hexahedron

Octahedron

Dodecahedron

Icosahedron

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Shell-man

The Pythagorean theorem, or Pythagoras' theorem, relates the lengths of the three sides of a right triangle, and states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

There are many proofs of the theorem, dating back to Ancient Greek mathematician Pythagoras who is credited with its discovery. The above diagram shows one such geometric proof.

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Did you know...

...that Ostomachion is a mathematical treatise attributed to Archimedes on a 14-piece tiling puzzle similar to tangram?
...that some functions can be written as an infinite sum of trigonometric polynomials and that this sum is called the Fourier series of that function?
...that the identity elements for arithmetic operations make use of the only two whole numbers that are neither composites nor prime numbers, 0 and 1?
...that as of April 2010 only 35 even numbers have been found that are not the sum of two primes which are each in a Twin Primes pair? ref
...the Piphilology record (memorizing digits of Pi) is in excess of 67000 as of Apr 2010?
...with a Perrin number denoted P(i), i=1,2,3..., when i is prime then P(i) is composite, being divisible by i?
...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 behavorial examples found in nature of ants, birds, bees, and fish among others?

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General	Foundations	Number theory	Discrete mathematics
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