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.

There are approximately 23540 mathematics articles in Wikipedia.

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Fourteen ways of triangulating a hexagon

The Catalan numbers, named for the Belgian Mathematician Eugène Charles Catalan, are a Sequence of Natural numbers that are important in Combinatorial mathematics. The sequence begins:

1, 1, 2, 5, 14, 42, 132, ...

The Catalan numbers are solutions to numerous Counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the n^th Catalan number is the number of full Binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associating n applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines.

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Image credit: User:Dmharvey

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Credit: Trekky0623

Missing square puzzle animation.

The missing square puzzle is an Optical illusion used in mathematics classes to help students reason about geometrical figures. It depicts two arrangements of shapes, each of which apparently forms a 13×5 right-angled Triangle, but one of which has a 1×1 hole in it.

The puzzle works as the blue and red triangles are not similar so their Hypotenuses are not Parallel. In one arrangement the line bends one way, in one arrangement it bends the other way, and the gap between these bent lines is exactly one unit.

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Did you know...

...that the primality of a number can be determined using only a single division using Wilson's Theorem?
...that the line separating the Numerator and Denominator of a Fraction is called a solidus if written as a diagonal line or a vinculum if written as a horizontal line?
...that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type the complete works of William Shakespeare?
... that there are 115,200 solutions to the Ménage problem of permuting six couples at a twelve-person table so that men and women alternate and are seated away from their partners?
... that Mathematician Paul Erdős called the Hadwiger conjecture, a still-open generalization of the Four-color problem, "one of the deepest unsolved problems in Graph theory"?
...that the six Permutations of the Vector (1,2,3) form a Hexagon in 3d space, the 24 permutations of (1,2,3,4) form a Truncated octahedron in four dimensions, and both are examples of permutohedra?
...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? This sum is called the Fourier series of that function.
...that outstanding mathematician Grigori Perelman was offered a Fields Medal in 2006, in part for his proof of the Poincaré conjecture, which he declined?

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General	Foundations	Number theory	Discrete mathematics
Mathematicians History of mathematics Philosophy of mathematics Mathematical notation Mathematical beauty Mathematics education Areas of mathematics List of basic mathematics topics Wikipedia Books: Mathematics	Foundations of mathematics Mathematical logic Set theory (portal) Naive set theory Axiomatic set theory Proof theory Model theory Recursion theory Category theory (portal) Topos theory Gödel's incompleteness theorems	Number theory (portal) Algebraic number theory Analytic number theory Arithmetic Numbers Natural numbers Prime numbers Rational numbers Algebraic numbers Fundamental theorem of arithmetic	Discrete mathematics (portal) Combinatorics Graph theory Game theory Discrete geometry Theoretical computer science Computability theory Complexity theory Information theory
Analysis	Algebra	Geometry and topology	Applied mathematics
Analysis (portal) Calculus Vector calculus Differential equations Calculus of variations Real analysis Complex analysis Functional analysis Measure theory Harmonic analysis Special functions Fundamental theorem of calculus	Algebra (portal) Elementary algebra Abstract algebra Group theory Ring theory Field theory Commutative algebra Geometric algebra Linear algebra Matrix theory Multilinear algebra Universal algebra Order theory Fundamental theorem of algebra	Geometry (portal) Topology (portal) General topology Algebraic topology Geometric topology Euclidean geometry Non-Euclidean geometry Affine geometry Projective geometry Differential geometry Riemannian geometry Lie groups Algebraic geometry Trigonometry	Applied mathematics Numerical analysis Mathematical biology Optimization Dynamical systems Chaos theory Financial mathematics Cryptography (portal) Mathematical physics Classical mechanics Probability Statistics (portal) Stochastic processes Operations research