Bottema Shatters Japan's Seclusion
Here's a curious Sangaku problem. Four squares are hinged as shown. When points A, B, C are collinear, what is the relationship between the sides of squares BEKH and KINS?
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Copyright © 19962018 Alexander Bogomolny
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We apply Bottema's theorem twice: to the pair of squares BEKH and AESX and to the pair BEKH and CHIY. The theorem yields two points U and V, such that triangles ABU, KSU, BCV, and IKV are right isosceles. It follows that K is the midpoint of segment UV and that
A more elegant solution appears on a separate page.
(Additional sangaku are listed below.)
References
H. Fukagawa, D. Pedoe, Japanese Temple Geometry Problems, The Charles Babbage Research Center, Winnipeg, 1989
Write to:
Charles Babbage Research Center
P.O. Box 272, St. Norbert Postal Station
Winnipeg, MB
Canada R3V 1L6 H. Fukagawa, A. Rothman, Sacred Geometry: Japanese Temple Geometry, Princeton University Press, 2008, p. 149
Sangaku

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Activities Contact Front page Contents Geometry
Copyright © 19962018 Alexander Bogomolny