At the women on the Go Expo (in Ringwood shopping center),
The contact phone number that I gave by hand writing might be wrong. I apologize for it. The contact detail on this website and also the information on my business card are right. Contact I put the three images in one section. To see each picture, Please click on the image. I will post another 'Sangaku' problem, soon.
(Please contact me by email or SMS if you are interested in the study session about 'Sangaku'.) Solution for 'Sangaku III' - Contd. Please See below. Please contact me by email or SMS if you are interested in the study session about 'Sangaku'.
Hi! Everyone🐧 I apologise that I didn't post the solution for 3 month. I was busy. Today I put the solution for the 'Sangaku III' . Please see below. The question is like this: See the left picture. The figure is made by that: fold a square paper (Blue and white color) like the left picture, and draw inscribed circles (Red one and Green one) into triangle parts. Now ‘χ’ is given there (lower-right of the figure). Express the diameter of red circle, the diameter of green circle and the length of one side of the square paper in terms of χ. The Answer is here: The diameter of Red circle is expressed by 2χ. The diameter of green circle is expressed by ( √2)χ. And The length of one side of the square is expressed by (3 + 2√2) χ. The solution is here: Continue to next blog.
June... It's winter here in Melbourne, and very cold in the morning. This month, I pick up the Sangaku at Kiryutenmangu. It's dedicated in 1852. The Kiryutenmangu is in Gunma prefecture, Japan. The description of some Sangaku problems are shown on a board. I take one problem form the 'sangaku'. It's like that. See the left figure. A square paper is folded and inscribed circles (Red and Green) are drawn into triangles. Now ‘χ’ is given there (lower-right of the figure). Express the diameter of green circle, the diameter of red circle and the length of one side of the square paper in terms of χ. The photo images from:
http://www.wasan.earth.linkclub.com/gunma/kiryutenmangu2.html http://www.wasan.earth.linkclub.com/gunma/tenmangukaisetu.png I have study session in Ringwood, Vic, Australia. Please contact me by email or SMS if you are interested. Contact It's very cold today, in Melbourne. How are you? Now, I put the solution for the problem which I showed in previous blog: "Sangaku (mathematics tablet) II". The question was like this: See the left figure. When the diameter of circumscribed circle (White) is given as D, Express the diameter of small circle (Red) in terms of D. (The 4 yellow circles are congruity.) The answer is: <The diameter of small circle (Red)> = D[(√2) – 1]² The solution is here: I will have more "Sangaku" maths problems to show. I might have some study sessions in Ringwood, Vic, Australia. Please contact me by email or SMS if you are interested. Contact This time, I introduce the mathematics tablet at “Isaniwa” shrine in Ehime prefecture. It was dedicated to the shrine in 1937. Please see the picture below. It is not too old. The problem is secondary school maths level. You might solve it easily. ☺✍ The problem is like that: See the left figure. When the diameter of circumscribed circle (White) is given as D, Express the diameter of small circle (Red) in terms of D. (The 4 yellow circles are congruity.) (I'll put the solution next time.) The photo: http://www.wasan.earth.linkclub.com/ehime/isaniwa22.html The reference: http://www.wasan.jp/index.html I have study session in Maroondah area (Ringwood, Ringwood East) Vic, Australia. Please contact me by email or SMS if you are interested. Now, I put the solution for the problem which I showed in previous blog: "Sangaku (mathematics tablet)". The question was like this: The three circles contact each other and also they are touching on a line, like left diagram. The diameter of the red circle is 9cm, and the diameter of the white circle is 36cm. Find the diameter of yellow circle. The answer is 4cm. The theorem (formula) written on the tablet is: <Diameter of yellow (small) circle> = [<Diameter of red (medium) circle> × < Diameter of white (large) circle>] / {[√<Diameter of red (medium) circle>] + [√< Diameter of white (large) circle>]}² I show the solution here. I have study session in Ringwood, Vic, Australia. Please contact me by email or SMS if you are interested.
Contact Reference: http://www.ene1.me.gunma-u.ac.jp/wasanken/gazou/satimiyaj-q2.jpg In Japan, during Edo period (1603-1867), people wrote mathematics problems on wooden tablet. The tablet was called ‘Sangau’. When the solutions were proved, people dedicated the Sangaku to a shrine or a temple and thanked the God for the discovery of theorem and solution. I intend to introduce various Sangaku in my blog. First one is a Sangaku at Sachimiya shrine in Gunma prefecture. The Sangaku was dedicated to the Sachimiya shrine in 1824. One of the problems is like this: The three circles contact each other and also they are touching on a line, like left diagram. The diameter of the red circle is 9cm, and the diameter of the white circle is 36cm. Find the diameter of yellow circle. You might have solved a similar problem in your secondary school. ✍
(I'll put the solution next time.) The reference (Japanese): http://www.ene1.me.gunma-u.ac.jp/wasanken/ (The photo image: http://www.ene1.me.gunma-u.ac.jp/wasanken/sangak-corner/satimiya1.htm ) |
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June 2017
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