Sacred Geometry: The Math of God

by Kya Swiftpaw Mon Jul 11, 2016 1:14 pm

Sacred Geometry Lesson 2: Phi Ratio and Why it is Important.

Hello again! Welcome to the next article on Sacred Geometry. If you haven't already read and watched the video do so now!

Now we're getting into some good stuff, math. I know some of you probably grimanced when you read that, but I assure you this is much more interesting than your averge algebra.

The golden ratio has been claimed to have held a special fascination for at least 2,400 years, though without reliable evidence. According to Mario Livio:

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. Euclid's Elements (Greek: Στοιχεῖα) provides the first known written definition of what is now called the golden ratio:

"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser."

Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e., the golden ratio. Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio.

The golden ratio is explored in Luca Pacioli's book De divina proportione of 1509.

The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as "about 0.6180340", was written in 1597 by Michael Maestlin of the University of Tübingen in a letter to his former student Johannes Kepler.

Since the 20th century, the golden ratio has been represented by the Greek letter φ (phi, after Phidias, a sculptor who is said to have employed it) or less commonly by τ (tau, the first letter of the ancient Greek root τομή—meaning cut).

Now enough of brief history, here is another video explaining more of the phi ratio in a way much more simpler than I could explain.

Enjoy!