Cracking a Japanese Sangaku Geometry Puzzle: A Tale of Radii
2025-09-20
A friend shared a Japanese Sangaku (geometric problems offered at shrines during the Edo period) puzzle: three mutually tangent circles inscribed in a square, finding the relationship between the small circle's radius and the square's side length. The author attempted a solution using coordinate geometry and calculus, but the algebra became too complex. Seeking help online, suggestions included Descartes' Circle Theorem and plane inversion. The inversion method simplified the problem, transforming arcs into lines, making the solution easier. The solution involved coordinate geometry, calculus, and inversion, highlighting the beauty and challenge of mathematics.