額 SAN GAKU Traditional Japanese Geometry SANGAKU In 17 century the Traditional Japanese Mathematics started and developed all over Japan ID: 275611
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Slide1
算 額 SAN GAKU
Traditional
Japanese Geometry.
SANGAKU
.Slide2
In 17 century, the Traditional Japanese Mathematics started and developed all over Japan. From 17th century to 20th century, many Japanese people enjoyed traditional Japanese mathematics.
Some
of them wanted to display his ability to the
other
people and they dedicated wooden tablets
to
shrines and temples on which
mathematics
problems
were drawn.
This
tablet is called as SANGAKU
.Slide3
SAN and GAKU implies Mathematics and Tablet, respectively. Now, about 900 SANGAKU have survived. Slide4
The size of the tablet is width 577cm & Height 91cm on which 23 problems were drawn. This tablet is so damaged, hung in 1881.Slide5
This big Sangaku of 1893 is no damaged since the tablet was hung inside of the temple. The size is width 368cm×height 114cm
.Slide6
The sangaku is hanging in the shrine and so beautiful. The size is 173cm width and 82cm height, hung in 1854．Slide7
This shrine is very small and there is no one. Inside of this shrine, the ceiling is so beautiful lattices. Slide8
The size of the lattice is 45cm by 45 cm.Fukagawa took the picture in face up.Slide9
.
Art
Mathematics
Sangaku: Art and MathematicsSlide10
In the same shrine another ceiling panel has a beautiful painting along with the mathematical problem. This is a good example of “Art and Mathematics”. The snake entwining the tree is “Art” and the writing in Japanese below it is “Mathematics”. The problem stated here is;A snake of the length 2 meter is sleeping in form of a circumference with the diameter. Then, find the diameter .
.Slide11
Supported by Asahi-newspaper-company SANGAKU Exhibition, 4/26-6/26, 2005.Held in Nagoya-city Science Museum. Editorial supervisor was Fukagawa HidetoshiSlide12
The fare; about 300000 USD, Big money Do you think ? How much money need for this exhibition ?Slide13
Big size Sangaku：４５３cm×１５１cm, in Yamagata.Slide14
Largest sangaku in Japan. ６２０cm×１４０cm. On this tablet, twenty two problems are written.Slide15
About thirty years ago, I visited this shrine to take photos of the biggest SANGAKU in Fukushima. I wanted to introduce it in this conference. The shrine is far from my home. Slide16
Replica sangaku reproduced by Atsuta shrine was hung in 1806. The width is 45cm and the height 30cm. In general case, Sangaku is challenging to visitors. Can you solve ?Slide17
Mathematician of TJM Moko Kitagawa (1763-1833） visited this shrine, recorded the problem and wrote his solution to the problem in his notebook which is extant. Following is two pages of his old notebook.Slide18
Replica Sangaku reproduced by Atuta shrine in Nagoya city. This tablet was hung in １８４１. The size is the width 45cm and the height 30cm. Find the relation on four circles..... Can you solve ? Result is
Slide19Slide20Slide21Slide22
Replica Sangaku of Atsuta shrine in Nagoya city. This tablet was hung in 1844. The size is the width 240cm and the height 60cm. Big size. Third problem from the right side is the same one on University Calculus course in Modern age. In general, sangaku problems are difficult.Slide23
Ordinary people enjoyed TJM. In the SANGAKU (1861), two ladies were enjoying TJM. The size is the width 170cm and the height 93cm.Teacher is teaching “Solve the high degree equation” to his friends.Women and Boys are trainng to handle soroban
People are discussing to do “SANGI”
Here is Mathematics problems
Sneeze. He seems getting a cold.Slide24
When a Rich trader ｅｎｄed his business work, He decided to learn “Mathematics” and “Poem” as his pastimes. And so he, right side, invited a Mathematician, left side. This is “Solving high degree equation” by means of “SANGI”. This aged rich trader dedicated the following sangaku to shrine. Slide25
This tablet is so beautiful, hung in 1873. The size is 162cm by 88cm. The frame is good art.DragonSlide26
Replica of 1813 sangaku by pottery.This problem is on an ellipse and three circles. Slide27
Sangaku was lost but the wooden model on this problem is found, at first, by Fukagawa in Meiji Yousui Museum.Slide28
This SANGAKU is the smallest in Japan and hung in 1779 at Rokusyo shrine of Aichi. The size is 50cm×25cm. Slide29
This is Rokusyo shrine in which the most small sangaku was hung in 1779.It is extant.Slide30
Japanese Temple Geometry, Sangaku is an interesting world of mathematics and art. This world developed by ordinary people, including mathematicians, who were love in mathematics, in 17th century to 20th century of Japan.Slide31
“Enjoy” is very important in mathematics. This world is useful in mathematics education, I believe. Many thanks for my talk. Hidetoshi Fukagawa.Slide32
終THE END