愛知県立春日井東高等学校 堀部 和経 HORIBE Kazunori URL httphoribejp Aichi Prefectural Kasugai Higashi S enior High School CAN YOU SOLVE THIS MATCH WITS AGAINST ID: 223717
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Slide1
Mathematical Beadwork
愛知県立春日井東高等学校
堀部 和経
HORIBE
Kazunori
URL http://horibe.jp
Aichi Prefectural
Kasugai
-Higashi S
enior High
SchoolSlide2
CAN YOU SOLVE THIS ?
MATCH WITS AGAINSTJAPANESE GEOMETRY
（日本の幾何学と知恵比べ）
Introduction to Japanese Geometry SANGAKUScientific AmericanMay 1998Slide3
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。Slide4
An illustration on the cover page of Scientific American
Sangaku
(mathematical wooden tablet)1788 in Edo(Tokyo) Prefecture.
It asks for the radiusof the -th largest blue circle in terms of ,the radius of the green circle.Sangaku problemSlide5
Hint ?
: The radius of t
he 5-th largest blue circle is .
Note that the red circles are identical, each with the same radius.Slide6
Other problems in sangaku
URL http://
horibe.jp
HDHDSlide7
Sangaku
(replica) W45cm-H30cm 1841 Atsuta
ShrineSlide8
Sangaku(Replica) W240cm-H60cm
dated on 1844 Atsuta Shrine
in Nagoya City of Aichi PrefectureSlide9
with Sonoda, Ono, and Fukagawa
Sangaku(replica)
at Atsuta Shrine 2013Slide10
Atsuta
Shrine
Slide11
Sangaku W330cm-H132cm 1830 (the genuine tablet)
Iwaifudou Temple in Chiba Pref.
Steiner Chain
HDSlide12
Iwaifudou
Temple in Chiba Pref.Slide13
W119cm-H37cm1877 Ishibe Shrinein Fukui Pref.
The
students were not only
Samurai but also children, women and chandlers. Wasan-Juku a private school for mathematics in the citySlide14
Private mathematics school
Studying the method of
an equation
StudyingarithmeticStudying how to do soroban, a Japanese abacusSlide15
Another Sangaku Problem
Dodecahedron with regular pentagons
Including an inscribed sphere
It asks for the ratio of the radius of the inscribed large spherein terms of the radius of the small sphare for pentagone.Slide16
Please
take a lookat the model in motion.
(gif animation) Slide17
算法助術 Sanpo-Jojutsu
1841 by Hiromu Hasegawa
The collection of mathematical formulae
of the Edo period.About 100 formulae are contained. Reprinted edition 2005Slide18
The problem appeared as one of the applied problems at the end of the
book. Slide19
30-ball problem in
Sanpo- JojutsuSlide20
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. Slide21
If the diameter
of Each small ball is305 sun,
what is the diameterof the large ball?
Sun (寸): a unit of the old Japanese lengthThe Answer is 682.000 sun.Slide22
Modeling
Cut along an
equatorial
planeSlide23
断面図
正１０角形
Regular decagon
正５角形
Regular pentagon
additional linesSlide24
How to solve the problemSlide25
Very strange
sunSlide26
Nagoya City Science Museum
The planetarium dome has a diameter of 35
m.Slide27
The large numbers 305 & 682 are chosen.
Why such large numbers ?Slide28
Next question Slide29Slide30
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 Gyuto Temple Shrine, Tokyo. Slide31
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. Slide32
Main Subject Mathematical Beadwork
My Work is
mathematical work???
or hobby work???Slide33
N=6
N=12
N=30Slide34
N=30
N=90
N=120Slide35
Semiregular polyhedron
N=30
N=90
N=120
N=210
N=270Slide36
Straight shape
Too simple
!Slide37
Helical shape Slide38
Y shapeSlide39
Torus shapeSlide40
Other Torus Slide41Slide42
Red coral Slide43
Tricolor
ringSlide44
Orthogonal
coordinate system
shapeSlide45
3D-hashtag character shape
「
3D井の字」Slide46
Tetrapod shapeSlide47Slide48
3D continuous tetrapod shapeSlide49
Regular dodecahedron shape Slide50Slide51
作品（１５）Slide52Slide53
作品（１６）Slide54Slide55Slide56
This model’s descriptionDiameter
= 38 mm was the former size of a
ping-pong ball. This wooden ball diameter is about 17 mm.
Diameter =
40 mm is the present size. Slide57Slide58
Mathematical Beadwork
model making of 30 ball problem
愛知県立春日井東高等学校
堀部 和経
HORIBE
Kazunori
URL http://horibe.jp
Aichi Prefectural
Kasugai
-Higashi S
enior High
SchoolSlide59
http://horibe.jp/PDFBOX/Manual_B30.pdfSlide60
Now, I will show you how to beadwork.
Steps
１，２Slide61
Steps ３，４Slide62
Steps ５，６Slide63
Steps ７，８Slide64
Steps ９，１０Slide65
Steps １１，１２Slide66
Steps １３，１４Slide67
Steps １５，１６Slide68
Steps １７，１８
URL http://
horibe.jp
HDSlide69
TriviaThe company name,
Nittaku, is not printed on the ball.
Because this is a custom-made ball by NIPPON TAKKYU
Co.,Ltd.
I think that no-logo balls are beautiful.I wish that the balls are former size.Slide70
No logo ping-pong
balls This work made with no logo ping-pong balls
was displayed in the lobby of Nittaku Co. Bld.
My treatureSlide71
Back to the
interrupted place
Ballstructure.comWB_MakingB.htmSlide72
Personal MemorandumSlide73
Personal
MemorandumSlide74
Personal Memorandum
That’s the point.This is the point I want to emphasize here.Please remember this point.Please
pay attention to the following.Let’s turn to the ・・・.Let me see.