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"Sangaku" - square and circles

"Sangaku" - square and circles

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship. Your mission, should you choose to accept it, is (1) to find the theorem behind the sangaku and (2) to prove it, of course. Some sangakus are fairly easy, others awfully hard. Good luck!

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship. Your mission, should you choose to accept it, is (1) to find the theorem behind the sangaku and (2) to prove it, of course. Some sangakus are fairly easy, others awfully hard. Good luck!

With the radius of the smaller circles as unit, find the radii of all others ?

With the radius of the smaller circles as unit, find the radii of all others ?

Apollonian Gasket.

Apollonian Gasket.

Second problem from the bottom right corner on the Katayamahiko shrine. A circle of radius r inscribes three circles of radius t, the centers of which form an equilateral triangle of side 2t. Find t in terms of r.

Second problem from the bottom right corner on the Katayamahiko shrine. A circle of radius r inscribes three circles of radius t, the centers of which form an equilateral triangle of side 2t. Find t in terms of r.

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship.

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship.

convergence tangent circles - Google Search

convergence tangent circles - Google Search

900e29d133cfdcce1c9472d6f7fead17.jpg (236×335)

900e29d133cfdcce1c9472d6f7fead17.jpg (236×335)

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship.

Sangakus form an ancient link between art and mathematics. These are japanese geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship.

art circles

art circles

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