摘要
用尺规作边数为3~2×2~n (n=0,1,…)的任意精度的正多边形,关键要找到5×2~k (k为整数和零)度中任意一角余弦的有理数的有限次平方根表达式,且与泰勒展开式等效。而当N于非2~r(r为自然数)形偶数和2^(2^5)十1形费尔马质数的2π/N角,这尚无规律可循。本文介绍的是20°余弦的表达式及其数学意义。
The key to drawing a regular polygon with arbitrary accuracy whose sides are 3~2×2~n (n=0, 1, ……) is to determine. an expression with limited dimension square root, which is cosine of an arbitrary angle from 5×2~k degree (k is an integrity basis or a zero), and this expression is supposed to equal Taylor's formula. However, if N is neither an even number as 2~r (r is a natural number) nor Fermat prime number as 2^(2^r)+1, 2π/N angles cannot be expressed. This paper gives an account of the expression of cos20°and its mathematical meanings.
