Mathematical Beadwork

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Mathematical Beadwok Intoduction to Japanese Geomety SANGAKU CAN YOU SOLVE

May 998 The aticle on Scientific Ameican begins with Of the wold s countless

tadition of sangaku, Japanese temple geomety.

cove page of Scientific Ameican Sangaku poblem It asks fo the adius of the

Sangaku (mathematical wooden tablet) 788 in Edo(Tokyo) Pefectue.

1 Mathematical Beadwok Intoduction to Japanese Geomety SANGAKU CAN YOU SOLVE THIS? 愛知県立春日井東高等学校 Aichi Pefectual Kasugai-Higashi Senio High School 堀部和経 HORIBE Kazunoi URL MATCH WITS AGAINST JAPANESE GEOMETRY ( 日本の幾何学と知恵比べ ) Scientific Ameican May 998 The aticle on Scientific Ameican begins with Of the wold s countless customs and taditions, pehaps none is as elegant, no as beautiful, as the tadition of sangaku, Japanese temple geomety. 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 illustation on the cove page of Scientific Ameican Sangaku poblem It asks fo the adius of the n-th lagest blue cicle in tems of, the adius of the geen cicle. Sangaku (mathematical wooden tablet) 788 in Edo(Tokyo) Pefectue. Note that the ed cicles ae identical, each with the same adius. Othe poblems in sangaku Hint? : The adius of the 5 th lagest blue cicle is n n URL HD HD

2 Sangaku(eplica) W45cm H30cm 84 Atsuta Shine Sangaku(Replica) W240cm H60cm dated on 844 Atsuta Shine in Nagoya City of Aichi Pefectue Sangaku(eplica) at Atsuta Shine 203 with Sonoda, Ono, and Fukagawa Atsuta Shine Sangaku W330cm H32cm 830 (the genuine tablet) Iwaifudou Temple in Chiba Pef. Iwaifudou Temple in Chiba Pef. 2

Studying the method of an equation Pivate

Poblem It asks fo the atio of the adius of

(gif animation) 算法助術 Sanpo Jojutsu 84 by

3 Studying the method of an equation Pivate mathematics school Wasan-Juku a pivate school fo mathematics in the city The students wee not only Samuai but also childen, women and chandles. W9cm H37cm 877 Ishibe Shine in Fukui Pef. Studying aithmetic Studying how to do sooban, a Japanese abacus Anothe Sangaku Poblem It asks fo the atio of the adius of the inscibed lage sphee in tems of the adius of the small sphae fo pentagone. Dodecahedon with egula pentagons Including an inscibed sphee Please take a look at the model in motion. (gif animation) 算法助術 Sanpo Jojutsu 84 by Hiomu Hasegawa The collection of mathematical fomulae of the Edo peiod. About 00 fomulae ae contained. The poblem appeaed as one of the applied poblems at the end of the book. Repinted edition

If the diamete of Each small ball is 305 sun, what is the diamete of the lage ball? Modeling The Answe is 682.000 sun.

4 このイメージは現在表示できません 30 ball poblem in Sanpo Jojutsu The desciption of the question As shown in the figue, the big ball is suounded by 30 small balls. The small balls touch each othe, and ae tangent to the suface of the inne big ball as well. If the diamete of Each small ball is 305 sun, what is the diamete of the lage ball? Modeling The Answe is sun. Sun ( 寸 ): a unit of the old Japanese length Cut along an equatoial plane 正 0 角形 Regula decagon 正 5 角形 Regula pentagon Ratio R 断面図 5 additional lines How to solve the poblem ( Fomula No.3 of Sanpo Jojutsu ) 角中径 5 面 2 diagonal 5 edge 2 R R 5 R Theefoe 5 R R 4

Vey stange small d 305 寸 LARGE D 682.000 寸 d 2, D 2R 寸 ( sun ) 30.3 mm( 日本 ) d 9m 24cm D 20 m 66cm They ae too big as a model. Nagoya City Science Museum The planetaium dome has a diamete of 35 m.

5 Vey stange small d 305 寸 LARGE D 寸 d 2, D 2R 寸 ( sun ) 30.3 mm( 日本 ) d 9m 24cm D 20 m 66cm They ae too big as a model. Nagoya City Science Museum The planetaium dome has a diamete of 35 m. 682 Actually , The lage numbes 305 & 682 ae chosen. Why such lage numbes? 682 High accuacy in ational numbe appoximation ,24, , ( Extension) Pell's equation x y 5 Solution x, y (305, 682) Next question Set x How to find thus x x x x 22 2 x x x x 4 零約術 ( Reiyaku jutsu) set : 0 x Notice: We know this poblem which was caied in the 830 book Sanpo-Kisho by Baba Seitoku (80-860). Accoding to the book, the poblem was witten on a mathematical tablet. In the book, Baba ecoded thity-six sangaku collected fom shines in Tokyo. The poblem was oiginally poposed by Ishikawa Nagamasa, a student of the school of Baba Seito ( ), who was Seitoku s fathe. It was witten on a tablet, which was hung in 798 in Gyuto Temple Shine, Tokyo. 5

Main Subject Mathematical Beadwok Pesonal

石川永政算法奇賞 (Sanpo kishyo)830 正督の息子馬場正統算法助術

6 Theefoe, it had aleady existed as a mathematical poblem in 798. Main Subject Mathematical Beadwok Pesonal Memoandum 算額 (Sangaku) 798 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)830 正督の息子馬場正統算法助術 (Sanpo jyojutsu)84 長谷川弘閲 My Wok is mathematical wok??? o hobby wok??? N=6 N=2 N=30 N=30 N=90 N=20 Semiegula N=270 polyhedon N=20 Staight shape N=30 N=90 N=20 Too simple! 6

7 Helical shape Y shape Tous shape Othe Tous Red coal 7

8 Ticolo ing Othogonal coodinate system shape Tetapod shape 3D hashtag chaacte shape 3D 井の字 3D continuous tetapod shape 8

9 Regula dodecahedon shape 作品 (5) 作品 (6) 9

10 This model s desciption Diamete = 38 mm was the fome size of a ping pong ball. This wooden ball diamete is about 7 mm 零約術 ( eiyaku jutsu) Diamete = 40 mm is the pesent size. Mathematical Beadwok model making of 30 ball poblem 愛知県立春日井東高等学校 Aichi Pefectual Kasugai-Higashi Senio High School 堀部和経 HORIBE Kazunoi URL Now, I will show you how to beadwok. Steps,2 0

11 Steps 3,4 Steps 5,6 Steps 7,8 Steps 9,0 Steps,2 Steps 3,4

12 Steps 5,6 Steps 7,8 URL HD Tivia The company name, Nittaku, is not pinted on the ball. My teatue No logo ping pong balls This wok made with no logo ping pong balls was displayed in the lobby of Nittaku Co. Bld. Because this is a custom made ball by NIPPON TAKKYU Co.,Ltd. I think that no logo balls ae beautiful. I wish that the balls ae fome size. Ballstuctue.com WB_MakingB.htm Pesonal Memoandum Back to the inteupted place 2

13 Pesonal Memoandum Pesonal Memoandum That s the point. This is the point I want to emphasize hee. Please emembe this point. Please pay attention to the following. Let s tun to the. Let me see. 3

OUR FIRST INSIGHT IN SANGAKU PROBLEMS

PROCEEDINGS OF SYMPOSIUM ON COMPUTER GEOMETRY SCG 0, VOLUME 0, OUR FIRST INSIGHT IN SANGAKU PROBLEMS Ivanka Stipančić-Klaić, Josipa Matotek Univesity of Osijek, Faculty of Civil Engineeing, Dinska 6a,