# Golden Section

2 3 The MysTery of Phi the golden thread of perennial wisdom The history of the golden section is difficult to unravel. Despite its use in ancient Egypt and the Pythagorean tradition, the first definition we have comes from Euclid 325265 BCE, who defines it as the division of a line in extreme and mean ratio. The earliest known treatise on the subject is Divina Proportione by Luca Pacioli 14451517, the monk drunk on beauty, and illustrated by Leonardo Da Vinci, who according to tradition coined the term sectio aurea, or golden section. However, the first published use of the phrase occurs in Martin Ohms 1835 Pure Elementary Mathematics. There are many names for this mysterious section. It is variously called a golden or divine ratio, mean, proportion, number, section or cut. In mathematical notation it goes by the symbol t, tau, meaning the cut, or more commonly or f, phi, the first letter of the name of the Greek sculptor Phidias, who used it in the Parthenon. So what is this enigmatic cut, and why is there so much fascination about it One of the eternal questions asked by philosophers concerns how the One becomes Many. What is the nature of separation, or division Is there a way in which parts can retain a meaningful relationship to the whole Posing this question in allegorical terms, Plato 427347 BCE in The Republic asks the reader to take a line and divide it unevenly. Under a Pythagorean oath of silence not to reveal the secrets of the mysteries, Plato posed questions in hopes of provoking an insightful response. So why does he use a line, rather than numbers And why does he ask us to divide it unevenly To answer Plato, we first must understand ratio and proportion. T a b le t o f S h am a sh , e a r ly 9 th C B C , S ip p a r , S I ra q