Dear All, Referring to the Golden Ratio and Sundials, Donald Snyder wrote:
I see nothing obvious except ... trivial possibilities. Try Googling Dodecahedral Sundial and you will see many examples. Here is one chosen at random: http://stretchingtheboundaries.blogspot.co.uk/2012/09/dodecahedral-sundial.ht ml The faces are all regular pentagons and the ratio of the distance between any two non-adjacent vertices and the length of a side is the golden ratio. Exercise for the reader: Come up with a simple proof of this! In some (slightly contrived) sense, a regular pentagon incorporates 25 instances of the Golden Ratio, so a Dodecahedron incorporates 300 such instances. Frank H. King Cambridge, U.K. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
