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arXiv 2609.25098math.HOmath.NT

在拉比 Abraham Ibn Ezra 和 Guru RSJ Reddy 的脚步下用根式逼近 Pi(及其他常数)

Approximating Pi (and other constants) by Radicals in the Footsteps of Rabbi Abraham Ibn Ezra and Guru RSJ Reddy

Doron Zeilberger

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中文总结 AI 辅助

受两位学者用根式逼近π的启发,本文指出其最优性并生成更多更优但不太简洁的根式近似。

中文摘要 AI 辅助

受博学家 Abraham Ibn Ezra(1089-1167)的启发,他用 20/9 乘以 2 的平方根来逼近 π,以及当代学者 RSJ Reddy 给出的 (14-√2)/4,我们指出这两个近似在某种意义下都是最优的,并且我们生成了许多其他更优的近似,尽管它们不那么简洁。

英文摘要

Inspired by the polymath Abraham Ibn Ezra (1089-1167) who approximated π by 20/9 times the square-root of 2, and contemporary scholar, RSJ Reddy, who gave (14-sqrt(2))/4, we point out that both of these approximations are optimal in some sense, and we generate many other ones that are even more optimal, albeit not as nice.

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