There are two kinds of creatures living in the flatland of Pentagonia: the Spires (S) and the Bones (B). They all have the shape of an isosceles triangle: the Spiers have an apical angle of 36o and the bones an apical angle of 108o.
Every year on Great Day of Division (September 11 - the day this Olympiad was held) they divide into pieces: each S into two smaller S's and a B; each B in an S and a B. Over the course of the year they then grow back to adult proportions. In the distant past, the population originated from one B-being. Deaths do not occur.
Investigate whether the ratio between the number of Spires and the number of Bones will eventually approach a limit value and if so, calculate that limit value. combinatoricscombinatorial geometry