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second proofs

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  • 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

  • Second Council of Lyons —     Second Council of Lyons (1274)     † Catholic Encyclopedia ► Second Council of Lyons (1274)     The Second Council of Lyons was one of the most largely attended of conciliar assemblies, there being present five hundred bishops, sixty abbots,… …   Catholic encyclopedia

  • 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

  • Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …   Wikipedia

  • Second voyage of HMS Beagle — The second voyage of HMS Beagle from 27 December 1831 to 2 October 1836 was the second survey expedition of HMS Beagle , under captain Robert FitzRoy who had taken over command of the ship on its first voyage after her previous captain committed… …   Wikipedia

  • Hilbert's second problem — In mathematics, Hilbert s second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic of real numbers is consistent.In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new… …   Wikipedia

  • List of mathematical proofs — A list of articles with mathematical proofs:Theorems of which articles are primarily devoted to proving them: See also: *Bertrand s postulate and a proof *Estimation of covariance matrices *Fermat s little theorem and some proofs *Gödel s… …   Wikipedia

  • Addition of natural numbers/Proofs — Mathematical proofs for addition of the natural numbers: additive identity, commutativity, and associativity. These proofs are used in the article Addition of natural numbers.DefinitionsThis article will use the definitions in addition of natural …   Wikipedia

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