Nārāyaṇa Paṇḍita 的 4 × 4 对角魔方图拉加蒂法

IF 0.1 Q4 HISTORY & PHILOSOPHY OF SCIENCE
Varuneshwar Reddy Mandadi, D. G. Sooryanarayan, K. Ramasubramanian
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引用次数: 0

摘要

对角线魔方在印度早在那迦朱那(Nāgārjuna,约公元 100 年)和瓦拉哈米希拉(Varāhamihira,约公元 550 年)时代就已为人所知。在《Gaṇitakaumud\(\bar{\iota }\》(约公元 1356 年)的《Bhadragaṇita》一章中,Nārāyaṇa Paṇḍita 对魔方进行了全面的数学研究,他简要概述了一种基于棋盘中的图拉嘎提或马的移动来构造 4 × 4 泛对角魔方的方法。在本文中,我们对 Nārāyaṇa Paṇḍita 的诗句进行了研究,发现了一种仅通过马步来构造 4 × 4 对角线方格的方法。我们还证明了这一算法能生成所有(且仅有)384 个阶为 4 的对角线正方形。除了介绍这种算法,本文还讨论了这些正方形所表现出的各种性质及其证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Turagagati method for 4 × 4 pandiagonal magic squares by Nārāyaṇa Paṇḍita

Turagagati method for 4 × 4 pandiagonal magic squares by Nārāyaṇa Paṇḍita

The pandiagonal magic squares have been known in India from the time of Nāgārjuna (c.100 CE) and Varāhamihira (c.550 CE). In his comprehensive mathematical study of magic squares presented in the Bhadragaṇita chapter of Gaṇitakaumud\(\bar{\iota }\) (c. 1356 CE), Nārāyaṇa Paṇḍita has briefly outlined a method for constructing 4 × 4 pandiagonal magic squares based on turagagati or horse movements in a chess board. In this paper, we present a study of the verses of Nārāyaṇa Paṇḍita which leads to a method of construction of 4 × 4 pandiagonal squares by horse moves only. We also show that this algorithm generates all (and only) the 384 pandiagonal squares of order 4. Besides presenting this algorithm, this paper discusses various properties exhibited by these squares along with their proofs.

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来源期刊
INDIAN JOURNAL OF HISTORY OF SCIENCE
INDIAN JOURNAL OF HISTORY OF SCIENCE HISTORY & PHILOSOPHY OF SCIENCE-
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