A determination of Catalan numbers in 18th century Italy by Giovanni Rizzetti (1675–1751)

IF 0.4 3区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

Historia Mathematica Pub Date : 2023-08-01 DOI:10.1016/j.hm.2023.07.002

Alessandro Belcastro, Giuseppina Fenaroli

引用次数: 0

Abstract

We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution.

Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined.

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Giovanni Rizzetti（1675–1751）对18世纪意大利加泰罗尼亚数字的测定

我们讨论了意大利学者Giovanni Rizzetti（1675–1751）面临的概率问题，并认为这是我们今天所称的“选票序列”的一个变体，加泰罗尼亚数字提供了一个解决方案。里泽蒂对解决方案的探索使他产生了一个迭代规则，其中涉及到加泰罗尼亚数字的考虑。尽管提出这些并不是他的最终目标，但他制定的规则允许他继续计算，只要他想。因此，这可能是第一次确定这样的数字。

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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来源期刊

Historia Mathematica 数学-科学史与科学哲学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

72 days

期刊介绍： Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.