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Easier Temple Geometry Problems
Problem 38 Dating from 1819, this problem comes from Yamaguchi Kanzan’s diary (chapter 7). We stick pins into the position of each vertex of a regular dodecagon (twelve sides), as shown figure 4.37. Then we take a string of length l = 150 cm and wrap it around the pins, as shown. This forms a small regular dodecahedron in the center. Find the length of the side s of the small dodecahedron. The solution is on page 136.
Figure 4.37. Find the side-length of the central dodecahedron in terms of the total length of the string.
Problem 39 This problem is the third one from the bottom left of the Katayamahiko shrine sangaku, color plate 5. A circle of radius R = 5 inscribes a regular pentagon of side a. Find a. Answer: a = 5.87. On page 137 we give a traditional solution from the 1810 book Sanpo¯ Tensho¯ho¯ Shinan, or Guidebook to Algebra and Geometry, by Aida Yasuaki (chapter 3).