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The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean * polygonal number * a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3). * a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions. == Terminology == Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jakob Bernoulli's Ars Conjectandi,〔 the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made up of successive triangular numbers, etc. These turn out to be the binomial coefficients. In this usage the square numbers 4, 9, 16, 25 would not be considered figurate numbers when viewed as arranged in a square. A number of other sources use the term ''figurate number'' as synonymous for the polygonal numbers, either just the usual kind or both those and the centered polygonal numbers. 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「Figurate number」の詳細全文を読む スポンサード リンク
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