Mathematics of Takebe Katahiro and History of Mathematics in East Asia (建部賢弘の数学と東アジア数学史). Proceedings 2014 at Ochanomizu University, Tokyo, Japan

This volume is a collection of papers contributed by participants at the 'International Conference on Traditional Mathematics in East Asia and Related Topics' held August 25-30, 2014 at Ochanomizu University, Tokyo, Japan, which was one of the satellite conferences of the Seoul ICM 2014. The year 2014 also coincides with the 350th anniversary of the birth of Takebe Katahiro (1664-1739), one of the great mathematicians of the Edo period. In his honor, the conference was called the 'Takebe Conference 2014.'This volume is divided into four parts and an appendix. Part one is concerned with Takebe Katahiro, his mathematics and his times. The editors believe that wasan represents one phase of the mathematics of East Asia, especially of China, Japan and Korea, for which ancient Chinese mathematics served as a basis, and Chinese characters as a lingua franca. Part two concerns the old mathematics of Korea in the Joseon Dynasty. Part three treats the mathematics of Ancient China. Part four, finally, follows the subsequent development of Japanese mathematics and mathematical education after the Meiji Restoration (1868). The very substantial appendix contains English translations of three volumes (12, 17 and 19) of the Taisei Sankei (twenty volumes, 1711), a monograph written by the master mathematician Seki Takakazu and the two Takebe brothers, Kata'akira and Katahiro.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America The Kyōhō Map of Japan. Originaly owned by Matsura Seizan -- Now conserved in the Moriya Hisashi Collection 建部賢弘生誕350周年 -- Takebe Conference 2014 Preface Program August 25, 2014 (Monday) August 26, 2014 (Tuesday) August 27, 2014 (Wednesday) August 28, 2014 (Thursday) August 29, 2014 (Friday) August 30, 2014 (Saturday) Editorial notes CONTENTS I. Takebe Katahiro and his Times Tsukane Ogawa (小川束), Takebe Katahiro - A man of his times: a survey of his life and mathematical thought §1. Introduction §2. The Life and Works of Takebe Katahiro §3. Mathematical Works of Takebe Katahiro §4. Mathematical Thought of Takebe Katahiro § Appendix References Kenji Ueno (上野健爾), Seki Takakazu and Takebe Katahiro - Two different types of mathematicians §1. Introduction §2. Mathematics of Seki §3. Mathematics of Takebe §4. Conclusion References Eberhard Knobloch, On the relation between point, indivisible, and infinitely small in western mathematics §1. Introduction §2. Ancient patterns §3. Circles and points: Viete, Kepler and his critics §4. Galileo's Discorsi §5. Leibniz's reading of Galileo §6. Leibniz's process of gaining insight §7. Epilogue References Chikara Sasaki (佐々木力), Takebe Katahiro's inductive methods of numerical calculations in comparison with Jacob Bernoulli's Ars Conjectandi of 1713 §1. Introduction §2. General Characteristics of Japanese Mathematics (Wasan) during the Edo Period, and Takebe Katahiro's Place in It §3. Takebe Katahiro's Tetsujutsu Sankei of 1722 §4. An Attempted Comparison with the Infinitesimal Mathematics in Early Modern Europe §5. Jacob Bernoulli's Ars Conjectandi of 1713 as a Frame of Reference for Reinterpreting Takebe's Thought §6. Takebe's Searching for the Chinese Origins of His Infinitesimal Mathematics §7. What Is Takebe's Art of Linking?: Preliminary Understanding §8. Contents of Takebe's Tetsujutsu Sankei §9. Takebe's Rivalry with His Admired Master Seki §10. Discourse on One's Own Proper Character §11. Takebe in the History of Early Modern Japanese Mathematics §12. Risks of Misunderstanding of Mathematics in Different Cultures §13. Towards an Intercultural Philosophy of Mathematics References Naoki Osada (長田直樹), Determinants by Seki Takakazu from the group-theoretic viewpoint §1. Introduction §2. Shuffles §3. Oblique multiplications §4. Notation and definitions in group theory §5. Shuffles and oblique multiplications from a group-theoretic viewpoint §6. A group-theoretical meaning of shuffles §7. Conclusion References Zelin Xu, Takebe Katahiro and the Shoushi Calendar §1. Introduction §2. Weaknesses in Takebe's Studies of Astronomy and Calendars, and the Drawing of a Map of Japan §3. The Impact of the Shoushi Calendar on Seki and Takebe's Knowledge Creation §4. Takebe's Jujireki Gi Kai §5. Conclusion References Tatsuhiko Kobayashi (小林龍彦), Takebe Katahiro and Nakane Genkei §1. Introduction §2. The Official Tasks of Takebe Katahiro in the Period of the Eighth Shogun Tokugawa Yoshimune §3. Takebe Katahiro and Nakane Genkei as coworkers §4. Transmission of the Lisuan Quanshu and its Japanese Translation §5. Concluding Remarks References Rina Sa, A comparative study of the Huangyu Quanlantu and Takebe Katahiro's Kyōhō Map of the Whole of Japan §1. Introduction §2. Emperor Kangxi and the Drawing of the Huangyu Quanlantu §3. Shogun Yoshimune and the Drawing of the Kyōhō Map §4. Comparing Kangxi's Huangyu Quanlantu and the Kyōhō Map §5. Conclusion References II. Joseon Young Wook Kim, Mathematics of Joseon dynasty —about the Tianyuanshu— §1. Introduction §2. The history of mathematics in Joseon §3. Theory of equations §4. Martzloff's question and tianyuanshu of Hong Jeong-ha References Sung Sa Hong, Solving equations in the early 18th century East Asia §1. Introduction and history in the 17th century §2. Solving equations in the Shuli Jingyun §3. Solving equations in the Taisei Sankei §4. Solving equations in the Gu-il Jib References Jia-Ming Ying, Nam Byeong-gil (1820-1869): a Confucian mathematician and a "promoter" of mathematics in late Joseon period §1. Introduction §2. Nam Byeong-gilthe Confucian scholar/mathematician. §3. Nam Byeong-gil: the "promoter" of mathematics. §4. Concluding remarks. References III. China David Mumford, Assessing the accuracy of ancient eclipse predictions §1. Introduction §2. Models, old and new §3. The Shoushili §4. Simulation results §5. Shah's results on the Tantrasangraha §6. Speculation References Makoto Tamura (田村誠), On the Litian problem of bamboo slips of the Qin Dynasty collected by Peking University §1. Introduction §2. Litian problems of the Suanshu §3. Interpretation of the slip (04-081) §4. Concluding remarks References Shirong Guo, The methods of constructing magic squares in the Chinese book Sansan Dengshu Tu §1. Introduction §2. The Construction of Magic Squares of Odd Orders §3. The Construction of Magic Squares of Even Orders §4. Analyzing the Procedures for the Construction of Magic Squares §5. Traditional and Western Elements §6. The Place of the Sansan Dengshu Tu in World History References Zhigang Ji, Chinese mathematics and western mathematics integrated in the Tongwen Suanzhi §1. Introduction §2. From the Epitome Arithmaticae Practicae to the Tongwen Suanzhi §3. Analysis of some Supplementary Problems in the General Part §4. Comments and Conclusions References IV. Modern East Asia Wenlin Li, Some aspects of the mathematical exchanges between China and Japan in modern times §1. Introduction §2. Chinese Students Known to Have Studied Mathematics in Japan in the Early 20th Century §3. Influence: Some Remarks References Jun Ozone (‪小曽根 淳), On the table of trigonometric functions that was introduced first to Japan §1. Introduction §2. Surveying in the Edo period §3. Issues with Western surveying as handed down to Japan §4. Fortuitous appearance of new historical materials §5. Seeking the 90-page booklet §6. Trigonometric tables quoted from Pitiscus §7. Conclusion References Rosalie Joan Hosking, Solving Sangaku with traditional techniques §1. Introduction §2. The Kijimadaira Tenmangū Sangaku and the Sanpō Tenzan Shinan §3. Tenzan jutsu §4. The Kijimadaira Tenmangū Sangaku §5. Sanpō Tenzan Shinan Problem §6. Applying the Sanpō Tenzan Shinan working to the Kijimadaira Tenmangū Sangaku References Steffen Döll and Andreas M. Hinz, Kyū-renkan—the Arima sequence §1. Introduction §2. Arima Yoriyuki, the Seki school and the Shūki sanpō §3. The Chinese Rings §4. Integer sequences §5. Arima's sequence References Osamu Kota (公田蔵), Western mathematics on Japanese soil ―A history of teaching and learning of mathematics in modern Japan— §1. Western mathematics in Japan until the early Meiji era §2. The last three decades of the nineteenth century §3. The first half of the twentieth century §4. Concluding remarks References Harald Kümmerle, Hayashi Tsuruichi and the success of the Tohoku Mathematical Journal as a publication §1. Introduction §2. Quantitative analysis §3. Reasons for the dommance §4. Case study §5. Conclusion References Appendix. A Few Volumes of the Taisei Sankei (大成算経) Tsukane Ogawa (小川束) and Mitsuo Morimoto (森本光生), Methods for a circle, Volume 12 of the Taisei Sankei §1. Introduction §2. Transcription rule §3. Terminologies References §4. Translation ([12] Four Rates of the methods for circle) [12.1] Chapter 1 on the Rates for Circles 【Power of cut perimeters, Definite circumference, Definite rates】 [12.2] Chapter 2 on the Rates for Arcs [12.3] Chapter 3 on the Rates for Sphere 【Sliced volumes, Definite volume, Multiplicative rates】 [12.4] Chapter 4 on the Rate for Spherical Caps【Beginning of the procedure】 Mitsuo Morimoto (森本光生) and Yasuo Fujii (藤井康生), The theory of well-posed equations, Volume 17 of the Taisei Sankei §1. Introduction §2. Transcription rule §3. Terminologies References §4. Translation ([17] Solving Well-Posed Problems) [17.1] Chapter 1 on Visible Problems [17.2] Chapter 2 on Hidden Problems [17.3] Chapter 3 on Concealed Problems [17.4] Chapter 4 on Submerged Problems Mitsuo Morimoto (森本光生) and Yasuo Fujii (藤井康生), The fifteen examples of algebraic equations, Volume 19 of the Taisei Sankei §1. Introduction §2. Transcription rule §3. Terms in the 15 examples References §4. Translation ([19] Examples of Exhibition (First half)) Examples of Hidden Problems (9 problems) [Problem 19-01] [Problem 19-02] [Problem 19-03] [Problem 19-04] [Problem 19-05] [Problem 19-06] [Problem 19-07] [Problem 19-08] [Problem 19-09] Examples of Concealed Problems (6 problems) Simply Concealed Problems [Problem 19-10] [Problem 19-11] [Problem 19-12] Multiply Concealed Problems [Problem 19-13] [Problem 19-14] [Problem 19-15] CJK Glossary §1. Name of Place §2. Name of People 2.1. Chinese 2.2. Japanese 2.3. Korean 2.4. Western §3. Name of Periods §4. Name of Calendars §5. Name of Books 5.1. Chinese 5.2. Japanese 5.3. Korean 5.4. Western §6. Miscellany 6.1. Chinese 6.2. Japanese 6.3. Korean