1 Introduction


       Following Euclid’s "rule", the golden number (or golden section, mean, or ratio, or divine proportion, etc.) arises when a line segment of length f = (1+√5)/2» 1.618 is divided into two pieces of lengths 1 and 0.618… In the regular pentagonal star and the "regular" pyramid, the golden number is discovered too (see Fig. 1). These numerical properties got numerological interpretations in mythical circles, in as much that the denomination of "golden angle" of 36° was introduced in literature. Furthermore, since the proportion of consecutive Fibonacci terms 1, 1, 2, 3, 5, 8, … tends to f, the occurrence of f in many unpretentious proportions of 2 to 3, 3 to 5 and so forth is not surprising. In recent times, several authors pointed out that the occurrence of the golden section in Egyptian pyramids, Greek art, da Vinci’s work, in music, poetry, modern architecture and art must be considered with the greatest precaution. Most of these "justifications of the frequent occurrence" of the golden number do not relay on solid backgrounds, while their frequency depends on a personal interpretation.



The’ regular’ pentagonal star and Utah piramid with height = base×√f /2.