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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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By
Maria João Lagarto
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. Japanese Math, Japanese Temple, In The Town, No Se, Geometry, Door Mat, Temple
Japanese Math
Japanese Temple
In The Town
No Se
Geometry
Door Mat
Temple
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.
Hojiroya Shōeman hung this sangaku at the Sugrawara Tenman shrine of Ueno City in 1854. Sacred Geometry Symbols, Geometric Art, Sacred Geometry, Sake, Chalkboard Quote Art, Body Art
Sacred Geometry Symbols
Geometric Art
Sacred Geometry
Sake
Chalkboard Quote Art
Body Art
Mathematical Treasure: Japanese Temple Mathematics
Hojiroya Shōeman hung this sangaku at the Sugrawara Tenman shrine of Ueno City in 1854.
Sangaku from Io shrine, Osaka prefecture, year 1846, size 182x60cm Osaka, Tablet
Osaka
Tablet
Sangaku from Io shrine, Osaka prefecture, year 1846, size 182x60cm
three blue circles sitting on top of a wooden table
Coasters
Art
Sangaku at Katayamahiko Shrine
最新ニュース - 岐阜県養老町の歴史文化資源 Edo Era, Math Projects, 11 11, Edo Period
Edo Era
Math Projects
11 11
Edo Period
田代神社奉納算額|最新ニュース|岐阜県養老町の歴史文化資源
最新ニュース - 岐阜県養老町の歴史文化資源
Sangakus, las matemáticas sagradas de los samuráis - Historias de la Historia
Sangakus, las matemáticas sagradas de los samuráis
Sangakus, las matemáticas sagradas de los samuráis - Historias de la Historia
an abstract painting with green, red and yellow shapes in the center on a gray background
Japanese Shrines
Geometry Problems
Japanese Shrine
Slide Show
Equations
The Gap
Science And Technology
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