12X Spiral
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 eggs in a carton, 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. I started calling the 4 positions where these candidates reside 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.
Notes:
Building a spiral around a clock, with 12-segments in the rotation, puts multiples of 3 at {3,6,9,12}, multiples of at {4,8,12}, multiples of 2 at {2,4,6,8,10,12}, and primes at {1,5,7,11}.
Folksonomies: education mathematics patterns
Taxonomies:
/science/mathematics/arithmetic (0.427533)
/family and parenting/babies and toddlers (0.394937)
/law, govt and politics/politics/elections (0.299018)
Keywords:
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Entities:
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Concepts:
Prime number (0.948189): dbpedia | freebase | opencyc
Highly composite number (0.898673): dbpedia | freebase | yago
1 (0.715716): dbpedia | freebase | yago
2 (0.581798): dbpedia | freebase | yago
6 (0.580678): dbpedia | freebase | yago
Integer sequences (0.550880): dbpedia
12 (0.547544): dbpedia | freebase | yago
4 (0.487552): dbpedia | freebase | yago
1001 circles: Exploring the spiral multiplication table