Historia Mathematica最新文献

There is a prevalent claim in the literature examining the history of numbers and the development of number words that some African group (“Bushmen” or “Pygmies”) counts in a particular way, where their numerals are of the form 1, 2, 3, 2+2, 2+2+1, etc. Numerous forms of this claim are traced back to their original sources through an extensive search of the available literature. The author argues that the different forms can be traced back to two early sources, which have been misquoted and bastardized along the way.

The Mainardi-Codazzi equations (MCE) and the fundamental theorem of surface theory (FT) are regarded as crucial achievements in the development of surface theory. The paper offers an analysis of three papers by Bour, Codazzi and Bonnet, submitted on the occasion of the Grand Prix des Mathématiques (1859), in which the MCE and the FT were systematically employed to deal with applicability problems. Our analysis provides a new insight into the historical process leading to a recognition of the relevance of the MCE and the FT and helps explaining why previous contributions on the subject could go unnoticed for years.

In the preamble of the 1818 sangaku tablet of Sugino'o Shrine, the proposers acknowledged the help of an unnamed teacher/master in understanding and solving certain mathematical problems. Endō Tadashi argued that this unnamed teacher could be Saitō Naonaka (1773-1844). In this paper, we examine the famous travel diary of Yamaguchi Kanzan (?-1850) especially on his second trip to the Northeast. We compare the content of Yamaguchi's diary with the three problems of Sugino'o's tablet. Together with the timing of Yamaguchi's travel, we conclude that Yamaguchi Kanzan was likely the unnamed master mentioned in the preface of the Sugino'o Shrine sangaku.

This geometry problem rose to great prominence among Japan's mathematicians after it was posted on a sangaku in 1749. Several scholars presented solutions, most famously Ajima Naonobu in 1774. Here we present Ajima's celebrated solution, along with a modern interpretation of his analysis, which notably employs the computation of a determinant via cofactor expansion. This article consists, in large part, of a translation of a modern Japanese language reconstruction of Ajima's solution. Some historical context is also provided.

Fukagawa and Rothman introduced a difficult wasan problem concerning an ellipse inscribed in a right triangle from an old travel diary. Like the famous Gion Shrine problem, it does not specify numerical data but asks only for an equation of a particular kind; moreover, modern solutions of the problem entail polynomial equations of degree greater than four. One may therefore wonder whether the problem was recorded correctly. A careful examination of the primary text suggests that problem may have been written in haste, and that the original problem may have been more tractable mathematically.

We analyze the work on geometrical optics by Felice Casorati who contributed to the dissemination of Gaussian optics in Italy. In his approach to Gauss's (1840) Untersuchungen he applied determinants to describe multiple refractions in an optical system and he explored the extension of the theory to cover slightly non-centered optical systems for which he introduced the cardinal line, a straight line that replaces the optical axis in this framework.