# Sangaku

Japanese Temple Mathematics
- Sangakus form an ancient link between art and mathematics. Geometrical images, abundantly decorated on wooden tablets, representing a mathematical theorem or relationship.

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The sangaku above was hung in 1800 in the Mizuho Shrine in the town of Shimotakaigum. The third problem from the right in translation and modern notation reads as follows [Sacred Mathematics, p. 146]: A trapezoid has lower side b, upper side a, and height h. Divide the area of the trapezoid into n small trapezoids of equal area. Call the lowest side of the smallest trapezoid k. Find n in terms of a, b and k.

Bridging the Gap Between Math and Art [Slide Show]

"Klein Sangaku," by Jean Constant. (Sangaku were geometry problem offerings at Japanese shrines.) "In a square PQRS, there are 2 circles touching SP & the incircle of the square, where 1 touches PQ and the other touches RS. Let A be the point of tangency of QR and the incircle & let the tangents of the 2 small circles through A intersect the segment SP at B & C. Given the inradius of the square, find the inradius of the circle in the triangle ABC." Solution at link