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Proofs from THE BOOK — is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to The Book in which God keeps all of the most elegant proofs of mathematical theorems. During a… … Wikipedia
Proofs of trigonometric identities — are used to show relations between trigonometric functions. This article will list trigonometric identities and prove them.Elementary trigonometric identitiesDefinitionsReferring to the diagram at the right, the six trigonometric functions of… … Wikipedia
Proofs and Refutations — is a book by the philosopher Imre Lakatos expounding his view ofthe progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the… … Wikipedia
Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are … Wikipedia
Proofs of Fermat's theorem on sums of two squares — Fermat s theorem on sums of two squares asserts that an odd prime number p can be expressed as: p = x^2 + y^2with integer x and y if and only if p is congruent to 1 (mod 4). The statement was announced by Fermat in 1640, but he supplied no proof … Wikipedia
Proofs of Fermat's little theorem — This article collects together a variety of proofs of Fermat s little theorem, which states that:a^p equiv a pmod p ,!for every prime number p and every integer a (see modular arithmetic). Simplifications Some of the proofs of Fermat s little… … Wikipedia
Proofs involving the totient function — This page provides proofs for identities involving the totient function varphi(k) and the Möbius function mu(k).um of integers relatively prime to and less than or equal to n Claim::sum {1le kle n atop {gcd(k,n)=1 k = frac{1}{2} , varphi(n) ,… … Wikipedia
Proofs involving the ellipse — The derivation of the cartesian form for an ellipse is simple and instructive. One simple definition of the ellipse is the locus of all points of the plane whose distances to two fixed points(called the foci) add to the same constant . See… … Wikipedia
proofs for the existence of God — This term (from the Latin probare, meaning to prove ) generically refers to theoretical arguments that are intended to lead to a particular conclusion. In Christian history, theologians have proposed many different types of proofs for the… … Glossary of theological terms
proofs — proof … Philosophy dictionary
