散文網(wǎng) » 科技 »學(xué)習(xí) » 【趣味數(shù)學(xué)題】正方形的對(duì)角線

【趣味數(shù)學(xué)題】正方形的對(duì)角線

2021-08-08 16:18 作者:AoiSTZ23 0人讀過(guò) | 我要投稿

鄭濤 (Tao Steven Zheng) 著

【問(wèn)題】

這個(gè)圓形的泥板來(lái)自《耶魯?巴比倫泥板書收藏集》，名為YBC 7289，寫于公元前1800年 – 1600年左右。它顯示了正方形及其對(duì)角線的幾何圖形。這個(gè)問(wèn)題要求邊長(zhǎng)為30的正方形的對(duì)角線之長(zhǎng)度。此泥板上以2的平方根為 ? $%7B(1%3B24%2C51%2C10)%7D_%7B60%7D$ 。

用 60 進(jìn)位數(shù)來(lái)計(jì)算出對(duì)角線的長(zhǎng)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.

【題解】

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