mathematical beadwork 愛知県立春日井東高等学校 堀部 和経 horibe kazunori url aichi...
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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 Senior High School
CAN YOU SOLVE THIS ?
MATCH WITS AGAINSTJAPANESE GEOMETRY(日本の幾何学と知恵比べ)
Introduction to Japanese Geometry SANGAKU
Scientific AmericanMay 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 (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.
nr
Sangaku problem
Hint ? : The radius of the 5-th largest blue circle is .
Note that the red circles are identical, each with the same radius.
95
r
22 1 14
n
rr
n
Sangaku(replica) W45cm-H30cm 1841 Atsuta Shrine
ProblemDate AnswerNames
Sangaku(Replica) W240cm-H60cm dated on 1844
Atsuta Shrine in Nagoya City of Aichi Prefecture
with Sonoda, Yamauchi, Jin, Fukagawa and
Horibe
Sangaku(replica) at Atsuta Shrine 2014
It is a heavy tablet.
Sangaku(replica) at Atsuta Shrine 2014
Atsuta Shrine
Sangaku W330cm-H132cm 1830 (the genuine tablet)
Iwaifudou Temple in Chiba Pref. Steiner Chain
HD
Iwaifudou Temple in Chiba Pref.
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 city
Private mathematics school
Studying the method of an equation
Studyingarithmetic
Studying how to do soroban, a Japanese abacus
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.
Please take a lookat the model in motion.(gif animation)
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 2005
The problem appeared as one of the applied problems at the end of the book.
30-ball problem in Sanpo- Jojutsu
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 is305 sun, what is the diameterof the large ball?
Sun ( 寸 ): a unit of the old Japanese length
The Answer is 682.000 sun.
Modeling
Cut along an equatorial plane
断面図
5
5
5R
Ratior
正10角形 Regular decagon 正5角形Regular pentagon
additional lines
How to solve the problem( ormula No.3 of )
1 5
2
F Sanpo Jojutsu
角中径面
1 5
2 2
r R
r
Therefore 5R
r
diagonal 1 5
edge 2
r
r
r
R
r
r
r
R 1 1 5
R
r
Very strange
9 24d m cm
682.000LARGE D 寸 30.3 mm ( )≒寸 (日本)
305small d 寸
20 66D m cmThey are too big as a model.
2 , 2d r D R
sun
Nagoya City Science Museum
The planetarium dome has a diameter of 35 m.
Jin & HoribeMay-11-2014
6825
305≒
22682 465,124 , 305 5 465,125
22( ) Pell 's equation 5 1Extension x y
Solution , (305, 682)x y
High accuracy in
rational number approximation
682Actually 5 2.236068 , 2.236066
305
The large numbers 305 & 682 are chosen. Why such large numbers ?
Next question 682
How to find 5305
≒
5
1 12 5 2
22 5
Set x
thus xx
12
2x
x
1
21
2 22 x
1 1 12 2 2
1 1 174 4 4
1 4 724 41 1744
72 6822
305 305
x
≒
1 1 12 2 2
1 12 4 412 4
14
4
xx
x
( )
: 0
Reiyaku jutsu
set
零約術 0
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.
① 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
② 算法奇賞 (Sanpo-kishyo)1830正督の息子・馬場正統
③ 算法助術 (Sanpo-jyojutsu)1841長谷川弘閲
Therefore, it had already existed as a mathematical problem in 1798.
①, ② areProblem & Answer.
③ is Problem, Answerand Solution.
Main Subject Mathematical Beadwork
My Work is
mathematical work???or
hobby work???
N=6N=12
N=30
N=30N=90
N=120
Semiregular polyhedron
N=30N=90
N=120
N=210N=270
Straight shape
Too simple !
Helical shape
Y shape
Torus shape
Other Torus
Red coral
Tricolor ring
Orthogonal coordinate system shape
3D-hashtag character shape 「 3D 井の字」
Tetrapod shape
3D continuous tetrapod shape
Regular dodecahedron shape
作品(15)
作品(16)
This model’s descriptionDiameter = 38 mm was the former size of a ping-pong ball. This wooden ball diameter is about 17 mm.
15 2
14
4 0
≒
Diameter = 40 mm is the present size.
( )reiyaku jutsu 零約術
4 382
17 17
38 405
17 17
40 mmpresent sizeWhite ball
38 mmformer size Orange ball
39
17
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 Senior High School
http://horibe.jp/PDFBOX/Manual_B30.pdf
The first step is very important.
Now, I will show you how to beadwork.
Steps 1,2
Steps 3,4
Steps 5,6
Steps 7,8
Steps 9,10
Steps 11,12
Steps 13,14
Steps 15,16
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.
No logo ping-pong balls This work made with no logo ping-pong ballswas displayed in the lobby of Nittaku Co. Bld.
My treature
Back to the interrupted place
Ballstructure.com
WB_MakingB.htm
Personal Memorandum
Personal Memorandum
• 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.