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Online Geometry Problem 1077: Chain of Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry. Level: High School, Honors Geometry, College, Mathematics Education


The figure shows a chain of n equal tangent circles of radius r. If S1 is the area of yellow shaded region and S2 is the area of blue shaded region, prove that S2 - S1 = 2πr2 .


Equal Tangent Circles, Circular Sector, Area, Sangaku, Sacred Geometry




Reference: Fukagawa Hidetoshi, Tony Rothman, Sacred Mathematics: Japanese Temple Geometry (Princenton University Press, 2008).
Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life—samurai, farmers, and merchants—inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan.


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Solution / Comment to Geometry Problem 1077
Last updated: Feb 8, 2015