Japanese Temple Geometry ProblemsA selection from the hundreds of problems in Euclidean geometry displayed on devotional mathematical tablets (Sangaku) which were hung under the roofs of shrines or temples in Japan during two centuries of schism from the west, with solutions and answers. |
Common terms and phrases
ABC is right-angled Aichi prefecture angle C₁ C₁(r centre chain of contact Chiba prefecture chord circle O(r circle O₁ r₁ circle O2 r2 circle which touches circles externally collinear contact circles described diameter ellipse externally ellipse O(a extant tablet Find r₁ Find the radius Fukusima prefecture given circle Ibaragi prefecture incircle of triangle internally intersects Iwate prefecture Japanese Temple Geometry longer extant loop of contact major axis Miyagi prefecture Nagano prefecture nally O1 r₁ O1 ri O₁(r O₁(ri P₁ perpendicular problem was written Problem written r4 in terms Sanpo scribed Show that r₁ shown square of side surviving tablet t₁ Tablet has disappeared Tablet has vanished tablet no longer tablet survives terms of r₁ ternally Theorem Tokyo prefecture touches AB touches BC touches CD touches O(r touches O₁ touches O₁(r₁ touches the ellipse triangle ABC Yamagata prefecture