1. Japanese Theorem -- From MathWorld According to an ancient custom of japanese mathematicians, this theorem was a Sangaku problem inscribed on tablets hung in a Japanese temple to honor the gods and http://mathworld.wolfram.com/JapaneseTheorem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Circles ... Polygons Japanese Theorem Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the triangulation chosen. This theorem can be proved using Carnot's theorem . In the above figures, for example, the inradii of the left triangulation are 0.142479, 0.156972, 0.232307, 0.498525, and the inradii of the right triangulation are 0.157243, 0.206644, 0.312037, 0.354359, giving a sum of 1.03028 in each case. According to an ancient custom of Japanese mathematicians, this theorem was a Sangaku problem inscribed on tablets hung in a Japanese temple to honor the gods and the author in 1800 (Johnson 1929). The converse is also true: if the sum of inradii does not depend on the triangulation of a polygon , then the polygon is cyclic Carnot's Theorem Cyclic Polygon Incircle ... search Hayashi, T. "Sur un soi-disant théorème chinois."

2. An Old Japanese Problem Geometry, first published in 1929 he reports (on page 193 of the Dover edition,1960) on the ancient custom by japanese mathematicians of inscribing their http://www.cut-the-knot.org/proofs/jap.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site R. Honsberger Mathematical Gems, III MAA, 1985, pp. 24-26 An Old Japanese Theorem In Roger Johnson's marvellous old geometry text- Advanced Euclidean Geometry , first published in 1929 - he reports (on page 193 of the Dover edition, 1960) on the ancient custom by Japanese mathematicians of inscribing their discoveries on tablets which were hung in the temples to the glory of the gods and the honor of the authors. The following gem is known to have been exhibited in this way in the year 1800. Let a convex polygon , which is inscribed in a circle, be triangulated by drawing all the diagonals from one of the vertices, and let the inscribed circle be drawn in each of the triangles. Then the sum of the radii of all these circles is a constant which is independent of which vertex is used to form the triangulation (Figure 1). A great deal more might have been claimed, for this same sum results for every way of triangulating the polygon! (Figure 2). As we shall see, a simple application of a beautiful theorem of L. N. M. Carnot

3. Title translating Western mathematics into Japanese. How had japanese mathematicians of the Tokugawa 18151887) were influencial. japanese mathematicians often coined terms using Chinese http://www.smhct.org/Programa Cientifico/simposio_desarrollo_sasaki.htm

Number: S 21 Title: "The Transmission of Scientific Cultures and the Formation of Scientific Languages" Organizers: Prof. Lewis Pyenson, (University of Louisiana, USA), Prof. Roshdi Rashed, (CNRS, France), and Prof. Sasaki Chikara, (University of Tokyo, Japan) ABSTRACTS Participants: Date: July 9th Room: C1, Palacio de Minería Roshdi Rashed The Translation of Greek Scientific Writings into Arabic Nobuo Miura The Transformation of Mathematical Terminology in the Middle Ages: Examples from Arabic into Latin and Italian Pascal Crozet Les stratégies des traducteurs scientifiques en Egypte au XIXe siècle: le cas des mathématiques Winfried Schröder The Role of Greman as a Language of Science Up To World War II in the Case of Meteorology and Geophysics Date: July 10th Room: C1, Palacio de Minería Shozo Motoyama The Formation of Terminology of Physical Science in Brazil Irina Podogorny The Establishment of a Common Language in the Archaeological Methods and Excavation in Argentina at the Turn of the 19th Century Alfredo Menéndez Navarro Internationalism, Nationalism and Information Science in Latin America

4. Japanese Mathematical History Japanese Mathematical History It is not until the start of the seventeenth centurythat definite historical records exist of japanese mathematicians. http://www.sunnyblue.net/tp/sangaku/jap_mat.html

Japanese History (1603-) Japanese Mathematics Sangaku Interactive Examples Japanese Mathematical History In Japanese the word wasan exists, it is used to refer to Japanese mathematics. Wassan is meant to stand in opposition to western mathematics, yosan.

5. Japanese Mathematics Japanese Mathematics Can you give me some information on Japanese mathematics, both past and present, and the names of some famous japanese mathematicians? Resendez http://rdre1.inktomi.com/click?u=http://mathforum.org/library/drmath/view/52583.

6. JAMI Background in 1954. Since the late 1950s, the department has entertained a steadyflow of young japanese mathematicians and students. A list http://mathnt.mat.jhu.edu/JAMI98-99/jamibackground.htm

Japan-U.S. Mathematics Institute (JAMI) Department of Mathematics Johns Hopkins University This Year's Conference: Shimura Varieties and Automorphic Forms Table of Contents Background and Goals Acknowledgements Programs Inaugural Conference (May 16-19, 1988) First Year (1988-89) Algebraic Analysis Second Year (1989-90) Algebraic K-Theory and Number Theory Third Year (1990-91) Complex Analysis and Algebraic Geometry Fourth Year (1991-92) Algebraic Topology and Conformal Field Theory Fifth Year (1992-93) Zeta Functions in Geometry and Number Theory Sixth Year (1993-94) Non-linear Elliptic and Parabolic Equations and Applications Seventh Year (1994-95) Linear and Non-linear Scattering Eighth Year Birational Geometry Ninth Year Elliptic Curves and their Applications ... Shimura Varieties and Automorphic Forms Fourteenth Year (2001-2002) Quantum Geometry in Dimensions 2 and 4. Governing Committees Photographs Background and Goals Since its founding in 1876 as the first graduate school in the United States, the Johns Hopkins University has had an international character and attracted young scholars and students from Japan. We are proud to mention Inazo Nitobe among them, who studied at Johns Hopkins for three years and whose friendship with Woodrow Wilson during that time is well known. The goal of JAMI is to foster friendly relationships between Japan and the United States; its academic purpose is to formalize and extend the long-existing relationship between the department and the Japanese mathematical community, and to use that relationship more generally to further mathematical interactions between the two countries.

7. JAMI Is Rapidly Developing An International Reputation, Both As A JAMI and operations have followed the original plan Each year we have selected aparticular field and invited several young japanese mathematicians working in http://mathnt.mat.jhu.edu/jami/programs.htm

JAMI is rapidly developing an international reputation, both as a mathematical center and as a focus for mathematical contact between Japan and the United States. The academic year Inaugural Conference (May 16-19, 1988) First Year Algebraic Analysis Second Year Algebraic K-Theory and Number Theory Third Year Complex Analysis and Algebraic Geometry Fourth Year Algebraic Topology and Conformal Field Theory Fifth Year Zeta Functions in Geometry and Number Theory Sixth Year Non-linear Elliptic and Parabolic Equations and Applications Seventh Year Linear and Non-linear Scattering Eighth Year Birational Geometry Ninth Year Elliptic Curves and their Applications ... Asymptotic and Effective Results in Complex Geometry

8. JAMI Pages Have Moved 1950s, the department has entertained a steady flow of young japanese mathematicians and students field and invited several young japanese mathematicians working in that field for http://www.math.jhu.edu/brochure1.html

Japan-U.S. Mathematics Institute (JAMI) Department of Mathematics Johns Hopkins University Pages have been moved to http://mathnt.mat.jhu.edu/JAMI98-99/jamibackground.htm . Please update your bookmarks. You will automatically be taken to the new location..... Please wait 15 seconds or click on the link above.

9. ICMAOSK Some Chinese mathematical books were republished and studied by japanese mathematicians,but these two books were not accessible to japanese mathematicians. http://www2.nkfust.edu.tw/~jochi/j9.htm

’†‘”Šw‘‚̊֍F˜a‚ւ̉e‹¿ é’n@–Î The Influence of Chinese Mathematics Arts on Seki Kowa Shigeru Jochi ABSTRACT CONTENTS ABSTRACTEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE 2 ACKNOWLEDGEMENTSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE 3 INTRODUCTION 1 : THE STUDY OF EDITIONS The Shu Shu Jiu Zhang EEEEEEEEEEEEEEEEEEEEEEE28 (a) Before completion of the Si Ku Quan Shu EEEEEEEEEE29 (b) From completion of the Si Ku Quan Shu to the publication of Yi-Jia-Tang Cong-Shu EEEEEEEEEE30 (c) After publication of the Yi-Jia-Tang Cong-Shu EEEEEEE33 (d) Conclusion to section 1-1EEEEEEEEEEEEEEEEE34 (2) The Yang Hui Suan Fa EEEEEEEEEEEEEEEEEEEEEEE35 (a) Versions of Qindetang press and its related editionsEEEE37 (b) Versions of the Yong Le Da Dian Edition EEEEEEEEEE42 (c) Conclusion to section 1-2EEEEEEEEEEEEEEEEE45 Notes EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE47 Diagram of manuscript tradition EEEEEEEEEEEEEEEEEEEE59 Biography of Ruan Yun and Li Rui EEEEEEEEEEEEEEEEEEEE62 2 : THE CONCEPTION AND EXTENSION OF METHOD FOR MAKING MAGIC SQUARE 3 : THE ANALYSIS FOR SOLVING INDETERMINATE EQUATIONS (1) Study history EEEEEEEEEEEEEEEEEEEEEEEEEE 148 (2) "The Sunzi Theorem" (Chinese Remainder Theorem)EEEEEEEEE 150 (a) In ChinaEEEEEEEEEEEEEEEEEEEEEEEEE 150 (b) In JapanEEEEEEEEEEEEEEEEEEEEEEEEE 156

10. Autobiography J. Fang going on in the name of Korean intellectual antiJapanese movement during the pre-War years to the entire community of japanese mathematicians, led by Iyanaga Shokitchi (b http://www.cnu.edu/phil/resources/autobiography.html

Philosophy Homepage Courses Schedule Registrar ... Contact Us Reference: J. Fang, Learning, East and West These are a few of his published works since 1945; which may help explain the nature of Learning, East and West, through his ‘intellectual journey’ ending with it (and a series of related works, forthcoming, including Docta Ignorantia, American Style, to appear late in 2002) Works by J. Fang in Chronological Order The Tragedy of Korea by F.A. McKenzie (tr. in Korean; Seoul, 1945). Right after the end of WW II (on 8.15), when there was hardly any paper to print anything, my cousin (editor of a left-leaning Seoul newspaper) helped me publish the above if only to prove what had been going on in the name of Korean intellectual ‘anti-Japanese’ movement during the pre-War years.   The English political reporter’s book was all about the ‘tragedy’ of Korea long before her annexation to Japan in 1910, then into the 1920s. And the ‘new Korean’ (way of spelling in phonetic alphabet – a revised version of the old, originally created in 14 th C., which H.G. Wells called the world’s best, most ‘scientific’ and the simplest) for my translation was the one, which had been devised for the new, forthcoming age, by the Korean Language Society, in itself a patriotic underground movement, some members of which died, or spent many years, in Japanese prisons.

11. Conclusion japanese mathematicians, however, only considered the mathematical interestof magic squares. Thus it was easier for japanese mathematicians http://www2.nkfust.edu.tw/~jochi/conc.htm

é’n@–Î Conclusion Shigeru Jochi Back to ICMAOSK Back to Home Page Back to Japanese Home Page Back to Chinese Home Page ... Back to English Home Page

12. Untitled field and invited several young japanese mathematicians working in that field for a departmental members but also with other American mathematicians. They have successfully used http://www.mathematics.jhu.edu/JAMI/programs.htm

JAMI is rapidly developing an international reputation, both as a mathematical center and as a focus for mathematical contact between Japan and the United States. The academic year Inaugural Conference (May 16-19, 1988) First Year Algebraic Analysis Second Year Algebraic K-Theory and Number Theory Third Year Complex Analysis and Algebraic Geometry Fourth Year Algebraic Topology and Conformal Field Theory Fifth Year Zeta Functions in Geometry and Number Theory Sixth Year Non-linear Elliptic and Parabolic Equations and Applications Seventh Year Linear and Non-linear Scattering Eighth Year Birational Geometry Ninth Year Elliptic Curves and their Applications ... Asymptotic and Effective Results in Complex Geometry

13. Math Digest Japanese Temple Geometry " by Tony Rothman, with cooperation of Hidetoshi Fukagawa many sangaku problems required calculus, and japanese mathematicians developed a crude form of it http://www.ams.org/new-in-math/mathdigest/199811-temple.html

Mathematical Digest Short Summaries of Articles about Mathematics in the Popular Press "Japanese Temple Geometry," by Tony Rothman, with cooperation of Hidetoshi Fukagawa. Scientific American , May 1998. During Japan's period of national seclusion (1639-1854) there arose a tradition known as sangaku , Japanese temple geometry. Under the roofs of their religious shrines and temples, sangaku devotees would hang brightly colored tablets engraved with solutions to geometry problems. While many of these problems could be solved with ordinary Eulidean geometry, others demanded more complicated mathematics. In fact, many sangaku problems required calculus, and Japanese mathematicians developed a crude form of it in the late 1600s, independently from their Western peers. The most difficult exercises are nearly impossible; today, modern geometers would use advanced techniques such as affine transformations to tackle them. While mathematically interesting, sangaku's cultural aspects could be even more intriguing. No one knows who began the tradition or why, but it is clear that followers created these tablets as acts of religious homage, and as challenges to other worshippers. Sangaku stands out as a distinctive Japanese tradition, and the tablets that have survived are regarded as elegant, beautiful works of art.

14. Samplematt3cangelosi about women mathematicians; students will recognize the contributions of japanese mathematicians in Wiles's Egyptian, Greek, Roman, Chinese, Japanese, Mayan, and Inca numeration http://www.coe.usu.edu/seced/graceweb/samplemath3cangelosi.htm

Amanda Cangelosi Trigonometry/Pre-Calculus (grades 10, 11, 12) Unit: Ethnomathematics Day 1 Objectives: -Students will become familiar with the origins/purposes of mathematics. -Students will understand the numerical system of ancient Babylonians and demonstrate their understanding by assigned exercises. -Students will understand the numerical system of ancient Egyptians and demonstrate their understanding by assigned exercises. Multicultural Dimensions: -Content Integration: Students are exposed to the mathematics of ancient Babylonians and Egyptians -Knowledge Construction: Students will learn different frames of reference and perspectives on mathematics. -Empowering School Culture: Mathematician research reports will be displayed in school halls. Time Instructional Strategies Technology/ Materials Assessment Methods ESL/Other Adaptations 20 min Lecture/Discussion : Teacher asks class why they do math as they do, concluding that math is a language; teacher asks where did math originate, and was it discovered, invented, or both? Teacher assigns a mathematician to groups of two students and explains that the groups are to research and present information to the class on their mathematician. List of mathematicians Formative: teacher will move around the room to make sure students are engaged, asking questions to all students.

15. Scientific American: Feature Article: Japanese Temple Geometry: May 1998 It is not until the opening of the 17th century that definite historicalrecords exist of any japanese mathematicians. The first http://www2.gol.com/users/coynerhm/0598rothman.html

Japanese Temple Geometry During Japan's period of national seclusion (16391854), native mathematics thrived, as evidenced in sangaku wooden tablets engraved with geometry problems hung under the roofs of shrines and temples by Tony Rothman , with the cooperation of Hidetoshi Fukagawa SUBTOPICS: Pleasing the Kami Wasan versus ... Spheres within Ellipsoids SIDEBAR: Works of Art Typical sangaku Problems ... RELATED LINKS Of the world's countless customs and traditions, perhaps none is as elegant, nor as beautiful, as the tradition of sangaku , Japanese temple geometry. From 1639 to 1854, Japan lived in strict, self-imposed isolation from the West. Access to all forms of occidental culture was suppressed, and the influx of Western scientific ideas was effectively curtailed. During this period of seclusion, a kind of native mathematics flourished. Devotees of math, evidently samurai, merchants and farmers, would solve a wide variety of geometry problems, inscribe their efforts in delicately colored wooden tablets and hang the works under the roofs of religious buildings. These sangaku , a word that literally means mathematical tablet, may have been acts of homagea thanks to a guiding spiritor they may have been brazen challenges to other worshipers: Solve this one if you can! For the most part

16. J J Fang Lèlàng in Chinese; Raku-ro in Japanese) culture and civilization, beginning in 108 (BCE, in Russian and German, and many japanese mathematicians; the latter, in the inimitable http://www.jjfang.com/

www.jjfang.com (jjjfang@verizon.net) J.J. Fang Life and Work Works, Past Abstract Algebra, Kant- Interpretationen , I, Numbers Racket: Aftermath of New Math, Bourbaki and Hilbert: Toward a Phil. of Mod.Math , I, II, Mathematicians from Ancient to Modern Times, I, The Literature of Mathematics Today: A Guide, Sociology of Mathematics and Mathematicians: Prolegom The Illusory Infinite – A Theology of Mathematics, Logic Today, Basics and Beyond, Nihonjin no Gogaku-kankaku (Japanese Linguistic Senses), 1983. Works, Present The Needham Question: Between Sociology The Birth of Exact Sciences: Btw. Sociology of Math., II, III Kant and Mathematics Today: Btw. Epistemol Sci Learning, East and West : A Lifelong Journey for Love of Wisdom, Athena, 2002. Docta Ignorantia – American-Style: The Institutionalized ‘Learned Ignorance’ in the Age of Information, Athena, 2003. Écrasez l’Infâme Against All Religious Wars! – A Secular Journey through the Theocratic West, Athena, 2003. Works, Future Terminating Terrorists Workable Thoughts Against Wars. Death, Math, and the Unknowable: Against the Dread of Death.

17. Scientific American: Feature Article: Japanese Temple Geometry: May 1998 The answer given here, though, was obtained by using the inversion method,which was unknown to the japanese mathematicians of that era. http://www2.gol.com/users/coynerhm/0598rothman_ans1.html

Answers to Sangaku Problems The original solution to this problem applies the Japanese version of the Descartes circle theorem several times. The answer given here, though, was obtained by using the inversion method, which was unknown to the Japanese mathematicians of that era. Because the method of inversion is generally not taught in American math courses, let us first review the technique and state without proof the results needed to solve the problem. Inversion is an operation generally defined with respect to a circle, call it S , with a radius k and a center T . The point T is called the center of inversion. Let P be any point in the plane containing S , and let TP be the legnth joining points T and P If P' is the inverse of P with respect to S , then TP (TP') = r In other words, r is the geometric mean of the lengths TP and TP' . The reason is that by construction, triangles TAP' and TAP are similar and so TP/r = r/TP' or TP (TP') = r Not only pointsbut entire figurescan be inverted. Each point P on the original inverts to P' on the inversion. The following four theorems apply to a circle

18. TMU GEOMETRY SERVER The Japanese version of the site contains information intended for japanese mathematicians. GENERALINFORMATION ON MATHEMATICS AND MATHEMATICIANS IN JAPAN. http://tmugs.math.metro-u.ac.jp/main.html

[Japanese version] WELCOME TO TMUGS ! The English version of this site contains general information on mathematics and mathematicians in Japan, and is directed towards a non-Japanese audience. The Japanese version of the site contains information intended for Japanese mathematicians. Both versions contain information related to the work of the geometry group at Tokyo Metropolitan University and collaborators. GENERAL INFORMATION ON MATHEMATICS AND MATHEMATICIANS IN JAPAN News, conferences, contact information, etc MATHEMATICS ONLINE (arXiv, Math Sci, online journals) WIKI/PPDG by Tatsuyoshi Hamada SOFTWARE 3DXM, CMCLAB, etc TMUGS EXHIBITION WHAT IS GEOMETRY? Some photographs of geometers... TMUGS Staff (includes contact information) LOCAL INFORMATION

19. Rm01-11 Out of 99 national universities and nearly 7000 tertiary education institutions,the consensus of the japanese mathematicians with whom I spoke is that about a http://www.nsftokyo.org/rm01-11.html

NATIONAL SCIENCE FOUNDATION TOKYO REGIONAL OFFICE September 5, 2001 The National Science Foundation's Tokyo Regional Office periodically reports on developments in Japan that are related to the Foundation's mission. It also provides occasional reports on developments in other East Asian countries. Tokyo Office Report Memoranda are intended to provide information for the use of NSF program officers and policy makers; they are not statements of NSF policy. Report Memorandum #01-11 T he S tate of M athematical S ciences in J apan The following report was prepared by B. Brent Gordon, Program Manager in the National Science Foundation's Division of Mathematical Science. Dr. Gordon traveled to Japan in July and August 2001 under a Japan Society for the Promotion of Science (JSPS) Short-Term Invitational Fellowship. Professor M. Hanamura at Kyushu University served as his host. A brief report on the research that Dr. Gordon conducted at Kyushu University appears as Special Scientific Report #01-03. He may be reached at bgordon@nsf.gov.

20. A Decade Of A Context-Sensitive Machine Translation System A Decad of a ContextSensitive Machine Translation System - Twojapanese mathematicians Approach -. 0. Introduction. In 1986 http://www1.rsp.fukuoka-u.ac.jp/chosho/decade_e.html

î•ñ”ŠwŒ¤‹†Žº ŽÄ“cŸªŒ¤‹†Žº A Decad of a Context-Sensitive Machine Translation System - Two Japanese Mathematicians' Approach - 0. Introduction. In 1986, (deceded) Toshio Ueno published a 315-line BASIC program of English-Japanese translation program [1], which can translate English sentences such as "This is a book which I bought yesterday." into the corresponding nice Japanese sentences. Ueno's program fascinated thousands of amateur machine translationists, among others the present author. The characteristics of Ueno's translation program is the integration of analysis part and generation part, which is a recursive procedure of local phrase translations. (to be continued) 1. The third generation free translation system. 2. The choice rules for the candidates of a translated word. 3. Context information. 3.1. The data. 3.2. Translation examples. 4. Dictionary architecture. 5. As a subject in the university education. 6. The first and the second language aquisition. > [1] T. Ueno: English-Japanese Translation Program for PC-9801 MS-DOS (in Japanese), PC Magajin, March (1986), p.71-88.

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