Hidden Universal Symmetry

Scott Onsott
Secrets In Plain Site

For millennia philosophers, mathematicians, architects, artists and mystics have been interested in the divine proportion, but its understanding has been highly fragmented. My recent work attempts to show how the divine proportion is a hidden universal symmetry worthy of comprehensive study and understanding.
Euclid’s book Elements (300 BCE) contains the first known written definition of the divine proportion, something he called the mean and extreme 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’s mean and extreme ratio is better known today as the golden mean, golden ratio or divine proportion. These names refer to the act of cutting a line at one uniquely important point. Point C cuts the line AB at the divine proportion if and only if the whole line (α+β) is in proportion to the longer segment (α) in exactly the same proportion as the longer segment (α) is to the shorter segment (β). 

The Greek letter Ф (phi) is used to denote the divine proportion. Ф is an irrational number whose decimal approximation continues forever without repeating. In fact, the divine proportion turns out to be “the most irrational number” of all. [1]

“Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel.” -Johannes Kepler (1571-1630)

Scientists are just recently starting to catch on to the divine proportion’s role in patterning the universe. 

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