Wasan Geometry
After giving a simple introduction of Japanese traditional mathematics called Wasan and Wasan geometry, we consider problems in Wasan geometry in details in three sections and show that the problems are rich source for mathematical study today, although m
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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wasan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wasan Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problems Involving Congruent Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Congruent Circles on a Line and a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Congruent Circles on a Line with Two Congruent Circles on a Line . . . . . . . . . . . . . . . . . . . Congruent Circles on a Line and Congruent Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Congruent Circles on a Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Congruent Circles on a Line with Two Intersecting Congruent Circles . . . . . . . . . . . . . . . . . Two Sets of Congruent Circles on a Line and Two Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . A Square and Three Congruent Circles in an Isosceles Triangle . . . . . . . . . . . . . . . . . . . . . . Congruent Circles in a Rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Arbelos in Wasan Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Sangaku Problems Involving a Circle of the Same Radius . . . . . . . . . . . . . . . . . . . . . . . Two Congruent Circles Touching a Perpendicular to AB . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Circles Touching a Perpendicular to AB at the Same Point . . . . . . . . . . . . . . . . . . . . . . Two Congruent Circles Touching an Inclined Line to AB . . . . . . . . . . . . . . . . . . . . . . . . . . . Congruent Circles Touching a Circle Passing Through the Center of α . . . . . . . . . . . . . . . . Reflection in the Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Golden Arbelos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arbelos with Overhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arbeloi Determined by a Chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Sangaku Problem Involving an Archimedean Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Sangaku Problem Involving Two Archimedean Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . Wasan Geometry and Division by Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Configuration A(1) . . . . . . . . . . . . . . . . . . . . . . . .
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