Wasan Geometry

Hiroshi Okumura ()
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Hiroshi Okumura: Graduate School of Engineering, Division of Life Science and Informatics, Faculty of Engineering, Department of Life science and Informatics

Chapter 25 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 711-762 from Springer

Abstract: Abstract After giving a simple introduction of Japanese traditional mathematics called Wasan and Wasan geometry, we consider problems in Wasan geometry in details in three sections and show that the problems are rich source for mathematical study today, although many people consider Wasan to be a historical mathematics. In the first section, we consider problems involving several congruent circles. Those figures have not been considered elsewhere, though they have interesting properties, and there are few expository writings dealing with those problems today. In the second section, we consider problems involving an arbelos formed by mutually touching three circles with collinear centers. Since it is one of the most well-known plane figures and has been studied by many mathematicians, it is a very good example to see the different approaches to studying the same figure between the East and the West. In the third section, we consider simple application of recently made definition of division by zero to Wasan geometry. At the end of this chapter, we see the practical side of Wasan and Wasan geometry briefly and give a simple history of the study of Wasan geometry.

Keywords: Wasan; Wasan geometry; Sangaku; Touching circles; Congruent circles on a line; Arbelos; Archimedean circle; Division by zero (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_122

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DOI: 10.1007/978-3-319-57072-3_122

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