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Pythagorean philosophers investigated the relationship of numbers extensively. They defined perfect numbers as those that were equal to the sum of all their divisors. For example: 28 = 1 + 2 + 4 + 7 + 14. [32] The theory of odd and even numbers was central to Pythagorean arithmetic. This distinction was for the Pythagorean philosophers direct ...
For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all. [5] The Pythagorean oath also mentioned the Tetractys: By that pure, holy, four lettered name on high,
In the Pythagorean method (which uses a kind of place-value for number-letter attributions, as does the ancient Hebrew and Greek systems), the letters of the modern Latin alphabet are assigned numerical values 1 through 9. [18]
Every non-negative real number is a square, so p(R) = 1. For a finite field of odd characteristic, not every element is a square, but all are the sum of two squares, [1] so p = 2. By Lagrange's four-square theorem, every positive rational number is a sum of four squares, and not all are sums of three squares, so p(Q) = 4.
Table of correspondences from Carl Faulmann's Das Buch der Schrift (1880), showing glyph variants for Phoenician letters and numbers. In numerology, gematria (/ ɡ ə ˈ m eɪ t r i ə /; Hebrew: גמטריא or גימטריה, gimatria, plural גמטראות or גימטריות, gimatriot) [1] is the practice of assigning a numerical value to a name, word or phrase by reading it as a number ...
In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c. [25] There exist infinitely many Pythagorean triples with square numbers for both the hypotenuse c and the sum of the legs a + b.
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
The letters d and elongated S were to be appropriated as operative symbols in differential calculus and integral calculus, and and in the calculus of differences. [24] In functional notation, a letter, as a symbol of operation, is combined with another which is regarded as a symbol of quantity. [24]