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2. Formulas for generating Pythagorean triples - Wikipedia

   en.wikipedia.org/wiki/Formulas_for_generating...

   To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ). Then its numerator and denominator are the sides, b and a, of a right triangle, and the hypotenuse is b + 1. For example:

3. Farey sequence - Wikipedia

   en.wikipedia.org/wiki/Farey_sequence

   In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.

4. Difference of two squares - Wikipedia

   en.wikipedia.org/wiki/Difference_of_two_squares

   Therefore, the linear factors are (+) and (). Since the two factors found by this method are complex conjugates, we can use this in reverse as a method of multiplying a complex number to get a real number. This is used to get real denominators in complex fractions. [1]

5. Fractionation - Wikipedia

   en.wikipedia.org/wiki/Fractionation

   [1] [2] Fractions are collected based on differences in a specific property of the individual components. A common trait in fractionations is the need to find an optimum between the amount of fractions collected and the desired purity in each fraction. Fractionation makes it possible to isolate more than two components in a mixture in a single run.

6. Factorization - Wikipedia

   en.wikipedia.org/wiki/Factorization

   The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

7. William Barnet, III - Pay Pals - The Huffington Post

   data.huffingtonpost.com/paypals/william-barnet-iii

   From January 2008 to July 2009, if you bought shares in companies when William Barnet, III joined the board, and sold them when he left, you would have a -64.4 percent return on your investment, compared to a -32.7 percent return from the S&P 500.