The mysterious numbers π and φ

This post concerns the two star-numbers of π and φ. Lots of myths have been created around these two numbers, many weird theories have been developed, while they have been the basic material for many books and movies. If the world of mathematics were a sky, then π and φ are definitely its most shiny stars. Π is the our familiar number of 3.14, the number that expresses the ration of the circumference of circle to its diameter. Π is infinite--i.e. its full length includes infinite decimal digits, and thus, according to a more mystical approach, it is the key that explains the world, relationships and even the market. One key that still stays well-hidden, since despite the fact that in the recent years the issue has undertaken championship dimensions--more than 51 billion digits have been discovered--number π still holds its secrets. Regarding φ, this is the so-called "number of the golden section" and its first digits are 1.61803. Similar to π, the golden section is a number whose decimal digits continue infinitely without any repetitive pattern. Nevertheless, it describes what many people throughout history have called "the ideal analogy". If one examines the paintings in the Louvre or Tate Gallery, one can observe that quite frequently, the artist selects a rectangle, that its sides have a ratio 1 over 1,61803. Through experiments, it has been verified that the height of an average human, compared to the distance from the feet to the navel has the same ratio. The golden section (or divine analogy) is a number that frequently appears in nature, in a mysterious fashion, and has been used in the construction of the Parthenon, and the Vitruvian Man of Da Vinci. We even encounter the ratio as an architectural dimension in the Pyramids, in the organic structure of Mozart's sonatas, in Beethoven's 5th Symphony etc...