Ebook: Seki, Founder of Modern Mathematics in Japan: A Commemoration on His Tercentenary

Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of Étienne Bézout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them.

The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in 2008. This book is the official record of the conference and includes supplements of collated texts of Seki's original writings with notes in English on these texts.

Hikosaburo Komatsu (Professor emeritus, The University of Tokyo), one of the editors, is known for partial differential equations and hyperfunction theory, and for his study on the history of Japanese mathematics. He served as the President of the International Congress of Mathematicians Kyoto 1990.

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Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of ?tienne B?zout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them.

The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in 2008. This book is the official record of the conference and includes supplements of collated texts of Seki's original writings with notes in English on these texts.

Hikosaburo Komatsu (Professor emeritus, The University of Tokyo), one of the editors, is known for partial differential equations and hyperfunction theory, and for his study on the history of Japanese mathematics. He served as the President of the International Congress of Mathematicians Kyoto 1990.

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Seki was a Japanese mathematician in the seventeenth century known for his outstanding achievements, including the elimination theory of systems of algebraic equations, which preceded the works of ?tienne B?zout and Leonhard Euler by 80 years. Seki was a contemporary of Isaac Newton and Gottfried Wilhelm Leibniz, although there was apparently no direct interaction between them.

The Mathematical Society of Japan and the History of Mathematics Society of Japan hosted the International Conference on History of Mathematics in Commemoration of the 300th Posthumous Anniversary of Seki in 2008. This book is the official record of the conference and includes supplements of collated texts of Seki's original writings with notes in English on these texts.

Hikosaburo Komatsu (Professor emeritus, The University of Tokyo), one of the editors, is known for partial differential equations and hyperfunction theory, and for his study on the history of Japanese mathematics. He served as the President of the International Congress of Mathematicians Kyoto 1990.

Content:
Front Matter....Pages i-xxvi
Front Matter....Pages 1-1
Seki Takakazu, His Life and Bibliography....Pages 3-20
Some Reflections on Main Lines of Mathematical Development....Pages 21-30
Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322....Pages 31-47
Archimedes in China: Archimedes and His Works in Chinese Literature of the Ming and Qing Dynasties....Pages 49-62
The Nine Chapters on the Mathematical Procedures and Liu Hui’s Mathematical Theory....Pages 63-88
On the Alternative Algorithm of the 7th Problem in the Sea Island Mathematical Canon....Pages 89-92
A Comparative Study on Traditional Mathematics of Korea and Japan....Pages 93-104
The Axes of Mathematical Methodology in the Song and Yuan Dynasties: The Construction of Mathematical Models....Pages 105-117
The Suanxue Qimeng and Its Influence on Japanese Mathematics....Pages 119-132
Power Series Expansions in India Around A. D. 1400....Pages 133-147
The Jink?ki of Yoshida Mitsuyoshi....Pages 149-172
R?sum? of Works on Mathematics of Seki Takakazu....Pages 173-186
Seki Takakazu’s Measuring Process of the Volume of Solids Derived from Spheres....Pages 187-192
Seki Takakazu’s Method on the Remainder Problem....Pages 193-206
Seki Takakazu’s Method of Calculating the Volume of Solids of Revolution and His Mathematical Object....Pages 207-218
Leibniz’s Theory of Elimination and Determinants....Pages 219-228
Algebra, Elimination and the Complete Book of Mathematics....Pages 229-244
Some Questions and Observations Around the Mathematics of Seki Takakazu....Pages 245-274
Ming Antu and His Power Series Expansions....Pages 275-297
Front Matter....Pages 299-310
Standing on the Shoulders of the Giant Influence of Seki Takakazu on Takebe Katahiro’s Mathematical Achievements....Pages 1-1
Takebe Katahiro’s Algorithms for Finding the Circular Arc Length....Pages 311-329
The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei....Pages 331-342
Manuscripts in the Edo Period: Preliminary Study on Manuscripts Written by Seki Takakazu....Pages 343-352
Influence of European Mathematics on Pre-Meiji Japan....Pages 353-355
On Contemporary Mathematics in Vietnam....Pages 357-374
Front Matter....Pages 375-383
Notes on Complete Book of Mathematics Vol. 4: Three Essentials....Pages 385-385
Complete Book of Mathematics Vol. 4: Three Essentials, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Fumiaki Ozaki and Hikosaburo Komatsu....Pages 387-392
Seki’s Trilogy: Methods of Solving Explicit Problems, Methods of Solving Implicit Problems and Methods of Solving Concealed Problems....Pages 393-435
Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 437-440
Methods of Solving Implicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 441-456
Methods of Solving Concealed Problems, by Seki Takakazu, collated by Hikosaburo Komatsu....Pages 457-468
Notes on Complete Book of Mathematics Vol.10: Geometry....Pages 469-494
Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu....Pages 495-498
Seki’s Theory of Elimination as Compared with the Others’....Pages 499-551
Back Matter....Pages 553-574
....Pages 575-588