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In geometry, a gnomon is a plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram; or, more generally, a figure that, added to a given figure, makes a larger figure of the same shape.〔.〕 ==Building figurate numbers== Figurate numbers were a concern of Pythagorean mathematics, and Pythagoras is credited with the notion that these numbers are generated from a ''gnomon'' or basic unit. The gnomon is the piece which needs to be added to a figurate number to transform it to the next bigger one.〔.〕 For example, the gnomon of the square number is the odd number, of the general form 2''n'' + 1, ''n'' = 1, 2, 3, ... . The square of size 8 composed of gnomons looks like this: To transform from the ''n-square'' (the square of size ''n'') to the (''n'' + 1)-square, one adjoins 2''n'' + 1 elements: one to the end of each row (''n'' elements), one to the end of each column (''n'' elements), and a single one to the corner. For example, when transforming the 7-square to the 8-square, we add 15 elements; these adjunctions are the 8s in the above figure. This gnomonic technique also provides a proof that the sum of the first ''n'' odd numbers is ''n''2; the figure illustrates 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「Gnomon (figure)」の詳細全文を読む スポンサード リンク
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