Despite all rational explanations, a number of enigmatic questions were raised by the subject of tiling a plane and filling a space, the answers to which have been pursued for centuries, just like the secret of “magic numbers”, behind which further mystical explanations were expected as to why these numbers are as special in nature as they are. The most perfect
shape (that with an infinite number of symmetries) is the circle. The sphere is a
body with similar characteristics. A special proportion, π, is attributed to both. Another mathematical proportion, the base number for the natural logarithm,
, is attributed to the perfectly swirling line, the logarithmic spiral. These numbers are made all the more mystical by the fact that, as delineators of proportion, they are independent of the scale chosen, that is they remain the same even when measured in different units — and it is in this scale invariance that their symmetry lies.