Untitled by Agnes Mezosi

Grether’s Spiral.

This is the comprehensive symmetrical spiral using all whole rational numbers based on the 12 positions of the standard clock, explaining the relationship between numbers. The first 12 numbers exist as positions creating patterns of behavior. All the numbers seems to fit 1 of 6 reflective pairs of positions.

This device leads to figuring out where numbers are placed in each of the 12 positions, by combing the divisibility rules. Every number has a place, and if we can figure out that place, we can figure out what the number’s divisors are. The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 inches in a foot, 12 months in a year, 24 hours in a day, 360 degrees in a circle, 60 seconds in minute? Because highly composite numbers can be divided evenly in many ways. For each 12 numbers in one ring around the spiral, there are 4 candidates to be prime. The 4 positions where these candidates reside are the prime fields: positions 1, 5, 7, and 11. When two prime numbers are separated by just one composite number, such as 5 and 7, 17 and 19, or 29 and 31, we call them twin primes.


Sherringham Park - 30/05/2016 by Matthew Dartford
Via Flickr: