Now, I put the solution for the problem which I showed in previous blog: "Sangaku (mathematics tablet)".
The question was like this:
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 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.
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.
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Reference: http://www.ene1.me.gunma-u.ac.jp/wasanken/gazou/satimiyaj-q2.jpg
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Reference: http://www.ene1.me.gunma-u.ac.jp/wasanken/gazou/satimiyaj-q2.jpg