“The foundation of Pythagorean Mathematics was as follows: The first natural division of Numbers is into EVEN and ODD. …

“They also noted that every number is one half of the total of the numbers about it, in the natural series; thus 5 is half of 6 and 4. And also of the sum of the numbers again above and below this pair; thus 5 is also half of 7 and 3, and so on till unity is reached; for the monad alone has not two terms, one below and one above; it has one above it only, and hence it is said to be the ‘source of all multitude.’

“‘Evenly even’ is another term applied anciently to one sort of even numbers. Such are those which divide into two equal parts, and each part divides evenly, and the even division is continued until unity is reached; such a number is 64. These numbers form a series, in a duple ratio from unity; thus 1, 2, 4, 8, 16, 32.” ~William Wynn Westcott

#### Odds Get Even

There is nothing strange or esoteric about dividing numbers first into odd and even. It is curious that some people consider one group to be better than the other for some reason. According to one psychological study, most people like odd numbers better than even ones. When asked to pick a favorite number between one and ten, nearly half chose seven. One study concluded that while even numbers feel calmer and more friendly, odd numbers are more exciting, more interesting.

#### Side by Side

That each number is half the sum of the two numbers closest to it is an interesting fact I had never noticed before. It is perfectly logical, of course. So in the number group 10, 11, 12; if you add en and twelve, you get 22. Half of 22 is eleven. Another thing to note here is that the companions of an odd number are even, while those of an even number are odd.

#### Evenly Even

The “Evenly Even” numbers are those which can be divided by two over and over until the result is one. The example given is “1, 2, 4, 8, 16, 32”. This sequence is more recognized today as the binary sequence used in modern computers. The quote is from an old book, so it is not surprising that it doesn’t mention this. Continue reading “Pythagorean Mathematics, Numbers and Cycles”