Kruh v egyptské matematice

Orientalia antiqua nova XXI:Sborník z vědeckého kolokvia pořádaného na Fakultě filozofické Západočeské univerzity v Plzni 30. dubna 2021 Pub Date : 1900-01-01 DOI:10.24132/zcu.2021.10392-1-14

Jindřich Bečvář

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Abstract

The article analyzes five exercises (R50, R48, R41, R42 and R43) from the Rhind Mathematical Papyrus (de-posited in the British Museum) that comes from the Second Intermediate Period of Egypt and is one of the best known examples of ancient Egyptian mathematics. One exercise (K2) from the Kahun Mathematical Papyrus (British Museum) is also discussed. The exercise R50 shows how Egyptian scribes calculated the area of a cir-cle with a given diameter. The exercise R48 compares the area of a circle with a given diameter to that of its cir-cumscribing square. Four other exercises demonstrate how to calculate the volume of a cylindrical grain silo with a given diameter and height. The author explains the algorithm which was used by Egyptian calculators. He also offers three ways how they could find a fairly accurate calculation, and how they approximated the value for π and compared Egyptian approximation with the approximation using by Babylonian scribes as well as Greek mathematicians.

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本文分析了五个习题(R50, R48, R41, R42和R43)，这些习题来自于埃及第二中期时期的莱茵数学纸莎草(保存在大英博物馆)，是古埃及数学最著名的例子之一。还讨论了来自Kahun数学纸莎草(大英博物馆)的一个练习(K2)。练习R50展示了埃及文士如何计算给定直径的圆的面积。练习R48比较具有给定直径的圆的面积与其周围的正方形的面积。另外四个练习演示了如何计算具有给定直径和高度的圆柱形粮仓的体积。作者解释了埃及计算器使用的算法。他还提供了三种方法，他们如何找到一个相当精确的计算，以及他们如何近似π的值，并将埃及近似值与巴比伦文士和希腊数学家使用的近似值进行比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Orientalia antiqua nova XXI:Sborník z vědeckého kolokvia pořádaného na Fakultě filozofické Západočeské univerzity v Plzni 30. dubna 2021

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