【趣味数学题】正方形的对角线

2021-08-08 16:18 作者:AoiSTZ23 0人读过 | 我要投稿

郑涛 (Tao Steven Zheng) 著

【问题】

这个圆形的泥板来自《耶鲁‒巴比伦泥板书收藏集》，名为YBC 7289，写于公元前1800年 – 1600年左右。它显示了正方形及其对角线的几何图形。这个问题要求边长为30的正方形的对角线之长度。此泥板上以2的平方根为 $%7B(1%3B24%2C51%2C10)%7D_%7B60%7D$ 。

用 60 进位数来计算出对角线的长度。

This circular clay tablet from the Yale Babylonian Collection, called YBC 7289, was created around 1800 – 1600 BCE. It shows the geometric diagram of a square with its diagonals. This problem asks for the length of the diagonal given the length of one side of the square being 30. The Babylonian tablet took the square root of 2 to be $%7B(1%3B24%2C51%2C10)%7D_%7B60%7D$ .

Calculate the length of the diagonal in base 60.

【题解】

$30%5Ccdot%7B(1%3B24%2C51%2C10)%7D_%7B60%7D%3D30%5Ccdot1%2B%5Cfrac%7B30%5Ccdot24%7D%7B60%7D%2B%5Cfrac%7B30%5Ccdot51%7D%7B60%5E2%7D%20%2B%5Cfrac%7B30%5Ccdot10%7D%7B60%5E3%7D%20$