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## Mathematical Beadwork

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**Mathematical Beadwork**Aichi Prefectural Kasugai-Higashi Senior HighSchool 愛知県立春日井東高等学校 堀部 和経 HORIBE Kazunori URL http://horibe.jp**Introduction to Japanese Geometry SANGAKU**CAN YOU SOLVE THIS ? MATCH WITS AGAINST JAPANESE GEOMETRY （日本の幾何学と知恵比べ） Scientific American May 1998**The article on Scientific American begins with**Of the world’s countless customs and traditions, perhaps none is as elegant, nor as beautiful, as the tradition of sangaku, Japanese temple geometry. 世界中の数え切れない習慣や伝統の中で、日本独自の幾何学を記した「算額」ほど優雅で美しいものは他に見当たらない。**An illustration on the cover page of Scientific American**Sangaku problem It asks for the radius of the -th largest blue circle in terms of , the radius of the green circle. Sangaku(mathematical wooden tablet) 1788 in Edo(Tokyo) Prefecture.**Note that the red circles are identical, each with the same**radius. Hint ? : The radius of the 5-th largest blue circle is .**Other problems in sangaku**URL http://horibe.jp HD HD**Sangaku(Replica) W240cm-H60cm dated on 1844AtsutaShrine in**Nagoya City of AichiPrefecture**Sangaku(replica) at Atsuta Shrine2014**with Sonoda, Yamauchi, Jin, Fukagawa and Horibe**Sangaku(replica) at Atsuta Shrine2014**It is a heavy tablet.**Sangaku W330cm-H132cm1830 (the genuine tablet) Iwaifudou**Temple in Chiba Pref. Steiner Chain HD**W119cm-H37cm1877 Ishibe Shrinein Fukui Pref.**Wasan-Jukuaprivate school for mathematics in the city The students were not only Samurai but also children, women and chandlers.**Private mathematics school**Studying the method of an equation Studying how to do soroban, a Japanese abacus Studying arithmetic**It asks for the ratio of the radius of the inscribed large**sphere in terms of the radius of the small sphare for pentagone. Another Sangaku Problem Dodecahedron with regular pentagons Including an inscribed sphere**Please take a look**at the model in motion. (gif animation)**算法助術Sanpo-Jojutsu1841 by Hiromu Hasegawa**The collection of mathematical formulae of the Edo period. About 100 formulae are contained. Reprinted edition2005**The problem appeared as one of the applied problems at the**end of the book.**The description of the question**As shown in the figure, the big ball is surrounded by 30 small balls. The small balls touch each other, and are tangent to the surface of the inner big ball as well.**If the diameter of**Each small ball is 305 sun, what is the diameter of the large ball? The Answer is 682.000 sun. Sun(寸): a unit of the old Japanese length**Modeling**Cut along an equatorial plane**断面図**正１０角形 Regular decagon 正５角形 Regular pentagon additional lines**Very strange**sun**The planetarium dome has a diameter of 35 m.**Nagoya City Science Museum Jin & Horibe May-11-2014**The large numbers 305 & 682 are chosen.**Why such large numbers ?**Notice:**We know this problem which was carried in the 1830 book Sanpo-Kisho by Baba Seitoku (1801-1860). Accoding to the book, the problem was written on a mathematical tablet. In the book, Baba recorded thirty-six sangaku collected from shrines in Tokyo. The problem was originally proposed by Ishikawa Nagamasa, a student of the school of Baba Seito (1777-1840), who was Seitoku’s father. It was written on a tablet, which was hung in 1798 in Gozu Temple Shrine, Tokyo.**Personal Memorandum**算額（Sangaku） 1798 東京都四谷区牛頭天王社 馬場正督の門人・石川永政 算法奇賞(Sanpo-kishyo)1830 正督の息子・馬場正統 算法助術(Sanpo-jyojutsu)1841 長谷川弘閲 Therefore, it had already existed as a mathematical problem in 1798.**Main Subject Mathematical Beadwork**My Work is mathematical work??? or hobby work???**N=30**N=12 N=6**N=120**N=90 N=30**Semiregular polyhedron**N=270 N=210 N=120 N=90 N=30**Straight shape**Too simple!