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Seki, Founder of Modern Mathematics in Japan

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Table of Contents

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    Book Overview
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    Chapter 1 Seki Takakazu, His Life and Bibliography
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    Chapter 2 Some Reflections on Main Lines of Mathematical Development
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    Chapter 3 Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322
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    Chapter 4 Archimedes in China: Archimedes and His Works in Chinese Literature of the Ming and Qing Dynasties
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    Chapter 5 The Nine Chapters on the Mathematical Procedures and Liu Hui’s Mathematical Theory
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    Chapter 6 On the Alternative Algorithm of the 7th Problem in the Sea Island Mathematical Canon
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    Chapter 7 A Comparative Study on Traditional Mathematics of Korea and Japan
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    Chapter 8 The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models
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    Chapter 9 The Suanxue Qimeng and Its Influence on Japanese Mathematics
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    Chapter 10 Power Series Expansions in India Around A. D. 1400
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    Chapter 11 An Early Japanese Work on Chinese Mathematics in Vietnam: Yoshio Mikami’s Study of the Vietnamese Mathematical Treatise Chi Minh Toan Phap
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    Chapter 12 The Jinkōki of Yoshida Mitsuyoshi
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    Chapter 13 Résumé of Works on Mathematics of Seki Takakazu
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    Chapter 14 Seki Takakazu’s Measuring Process of the Volume of Solids Derived from Spheres
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    Chapter 15 Seki Takakazu’s Method on the Remainder Problem
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    Chapter 16 Seki Takakazu’s Method of Calculating the Volume of Solids of Revolution and His Mathematical Object
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    Chapter 17 Leibniz’s Theory of Elimination and Determinants
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    Chapter 18 Algebra, Elimination and the Complete Book of Mathematics
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    Chapter 19 Some Questions and Observations Around the Mathematics of Seki Takakazu
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    Chapter 20 Ming Antu and His Power Series Expansions
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    Chapter 21 Standing on the Shoulders of the Giant Influence of Seki Takakazu on Takebe Katahiro’s Mathematical Achievements
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    Chapter 22 Takebe Katahiro’s Algorithms for Finding the Circular Arc Length
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    Chapter 23 The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei
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    Chapter 24 Manuscripts in the Edo Period: Preliminary Study on Manuscripts Written by Seki Takakazu
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    Chapter 25 Influence of European Mathematics on Pre-Meiji Japan
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    Chapter 26 On Contemporary Mathematics in Vietnam
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    Chapter 27 Notes on Complete Book of Mathematics Vol. 4: Three Essentials
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    Chapter 28 Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu
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    Chapter 29 Seki’s Trilogy: Methods of Solving Explicit Problems, Methods of Solving Implicit Problems and Methods of Solving Concealed Problems
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    Chapter 30 Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
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    Chapter 31 Methods of Solving Implicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
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    Chapter 32 Methods of Solving Concealed Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
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    Chapter 33 Notes on Complete Book of Mathematics Vol.10: Geometry
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    Chapter 34 Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu
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    Chapter 35 Seki’s Theory of Elimination as Compared with the Others’
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Title
Seki, Founder of Modern Mathematics in Japan
Published by
Springer, Tokyo, January 2013
DOI 10.1007/978-4-431-54273-5
ISBNs
978-4-43-154272-8, 978-4-43-154273-5
Editors

Eberhard Knobloch, Hikosaburo Komatsu, Dun Liu

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