Through many cultures, star polygons were used as sacred symbols with the star of David and the Sri Yantra Hindu patterns shown in Figure 1a and 1b as two examples. The fact that Venus traverses a five-pointed star over an eight-year cycle in the heavens as seen from the Earth, shown in Figure 1c, was known to ancient civilizations. Also the designs of ancient sacred geometry use a small vocabulary of proportions such as Ö 2, Ö 3, the golden mean t = (1+Ö 5)/2 and the silver mean q = 1 + Ö 2. I will show that all of these constants can be related to the edge lengths of star polygons and that they are ultimately related to a sequence of numbers called silver means the first of which is the golden mean. These silver means will also be shown to be generalizations of the imaginary number i in some sense. The geometry of the star heptagon will be found to be particularly interesting. I have previously shown that star polygons are also related to the chaotic dynamics of the logistic equation [Kappraff 2002].
Jay Kappraff
New Jersey Institute of Technology