翻訳と辞書 Words near each other ・ Square Peak ・ Square Peg in a Round Hole ・ Square peg in a round hole ・ Square Peg Media ・ Square Pegs ・ Square Pegs (disambiguation) ・ Square Pegs (Hong Kong TV series) ・ Square Pharmaceuticals ・ Square piano ・ Square Pie ・ Square planar molecular geometry ・ Square Pond ・ Square principle ・ Square pyramid ・ Square pyramidal molecular geometry ・ Square pyramidal number ・ Square René-Viviani ・ Square rig ・ Square Rock ・ Square Rock Dipping Vat ・ Square Rooms ・ Square root ・ Square root biased sampling ・ Square Root Day ・ Square root of 2 ・ Square root of 3 ・ Square root of 5 ・ Square root of a 2 by 2 matrix ・ Square root of a matrix ・ Square root of negative one Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Square pyramidal number ： ウィキペディア英語版 Square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base. Square pyramidal numbers also solve the problem of counting the number of squares in an grid. ==Formula== The first few square pyramidal numbers are: : , ... . These numbers can be expressed in a formula as :$P\_n\; =\; \backslash sum\_^nk^2\; =\; \backslash frac\; =\; \backslash frac.$ This is a special case of Faulhaber's formula, and may be proved by a mathematical induction.〔Hopcroft, Motwani & Ullman (2007), (p. 20 )〕 An equivalent formula is given in Fibonacci's Liber Abaci (1202, ch. II.12). In modern mathematics, figurate numbers are formalized by the Ehrhart polynomials. The Ehrhart polynomial of a polyhedron is a polynomial that counts the number of integer points in a copy of that is expanded by multiplying all its coordinates by the number . The Ehrhart polynomial of a pyramid whose base is a unit square with integer coordinates, and whose apex is an integer point at height one above the base plane, is .〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Square pyramidal number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.