Number Theory & Mysticism Part 1

This series was requested in another discussion. -S

Number Theory & Mysticism

This chapter explores relationships in numbers. Some are interesting, but appear to have no practical value. Who am I to say that nobody else will find practical use for what I see as useless? Let the reader decide. Some of the material is historical in nature. Make of it what you will.

Certain ancient Greeks looked for patterns in numbers. One remarked that "all is number." They had only integers at the time, which they used in making fractions. Odd numbers were considered male, and even numbers female. Triangular patterns could be made with dots numbering 3,6,10, and so on. The one with 10 dots was called the holy tetractys. Square patterns could also be made using 4,9,16, etc. The next higher one could be made by adding an L-shaped border called a gnomon (carpenter's rule). It was discovered that each odd number was the gnomon of a square number. For example, 7 dots are added to a square of 3 by 3 to make a square of 4 by 4. The number 1 was identified with reason; two with opinion (a person with two opinions wavers). The number 4 stood for justice, steadfast and square; five for marriage , the union of the first even with the first true odd number. Seven stood for the maiden goddess Athene 'because seven alone within the decade has neither factors nor product.' Today the number seven is considered lucky, and the number 13 unlucky. Could the latter be because Christ + 12 Apostles = 13?

It is worth noting that, in geometry, the number 1 came to be identified with the point, 2 with the line, 3 with the surface, and 4 with the solid. Today, with our dimension concept, we identify 1 with the line, 2 with the surface, and 3 with the solid. Which is better? One of the 5 regular polyhedrons, the dodecahedron, is roughly spherical and represented the universe.

For some numbers such as 6 and 28, the sum of the factors equals the number (6 = 1 + 2 + 3 and 6 = 1 * 2 * 3). These the Greeks called 'perfect' numbers. Many have tried to find a rule for finding all these numbers. Can you prove or disprove that no odd number has this property? Such endeavors are the essence of the theory of numbers.

Part 2 will be Prime Numbers.

S