“…1690 and has some interesting mathematical properties, such as its curvature, that varies linearly with the parameter s and it is thus the simplest example of a curve that can be constructed solely from its curvature. Recently, clothoids have been practically used for robotic control 8) and even for designing roller coasters. 9) Conversely, among the enigmatic numbers that Nature seems to enjoy, the golden mean, ¼ ð1 þ ffiffi ffi 5 p Þ=2 ¼ 1:618, attracted a great deal of attention from the ancient greeks, who even attributed a divine origin to such geometrical relationships, present in a wide variety of natural objects, 10,11) from seashells to sunflowers, fruits, patterns in the skins of animals and even human faces.…”