目の粗いグリッド・ボードに正多角形を作図する 初歩的な数学を用いた技法について

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  • About on the techniques that used basic mathematics to draw a regular polygons with simple ruler on large-scale Grid board
  • メ ノ アライ グリッド ・ ボード ニ セイ タカッケイ オ サクズ スル ショホテキ ナ スウガク オ モチイタ ギホウ ニ ツイテ

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We have drawn the special n square shapes(regular nth polygons ) by Euclidean geometry methods.But possible n is restricted as the multiple of power of 2 ,special prime numbers, 3,5,17,257,65337,…but they are square-free. If n tends to large , an accumulation error from methods of Euclid ,also grows big. Like in a problem of drafting, one draw regular 64th polygon, but that is an unrealistic demand even if it is for the train courteousness and patience feeling. In case regular nth polygon in an unit circle, we can draw them by diagonal line which join first top z0 and rth zr or one side, accompanied accumulated error specially which of the needle of compasses. In contrast, we can get x- coordinate of zr with necessary precision by a trigonometric function directly numerical value, but it becomes difficult to realize on the coordinated plane. We can improve it by use the method of continued fractions . Finally we adds roughly explanations for the case of regular 17polygon (heptadecagon ), regular 257th polygon (diacosipenta- -contaheptagon) drawn by Euclid method ,and the table of primitive root modulo p(prime) .

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