对希腊和印度确定球体表面积方法的评价

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2018-01-04 DOI:10.18311/JIMS/2018/18897

K. Mahesh, Aditya Kolachana, K. Ramasubramanian

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引用次数: 0

摘要

尽管希腊和印度文明都对数学的发展做出了巨大贡献，但他们处理各种问题的方法却大相径庭，无论是在所使用的技术还是在范围上。我们在确定球体表面积的背景下证明了这一点。虽然这个问题的解决方案在希腊传统中被认为是阿基米德（公元前3分），但印度传统中第一个幸存的证据可以在Bhāskara的Siddhāntaśiroma中找到ṇi（12美分。CE）。在本文中，我们讨论了阿基米德和巴斯卡拉所采取的方法，并从数学和教学的角度比较了他们的技术。

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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An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere

While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.