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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. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   A mixed number (also called a mixed fraction or mixed numeral) is the sum of a non-zero integer and a proper fraction, conventionally written by juxtaposition (or concatenation) of the two parts, without the use of an intermediate plus (+) or minus (−) sign. When the fraction is written horizontally, a space is added between the integer and ...

4. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

5. Algebraic fraction - Wikipedia

   en.wikipedia.org/wiki/Algebraic_fraction

   A rational fraction () is called proper if ⁡ < ⁡ (), and improper otherwise. For example, the rational fraction is proper, and the rational fractions + + + and + + are improper. Any improper rational fraction can be expressed as the sum of a polynomial (possibly constant) and a proper rational fraction.

6. Triple product - Wikipedia

   en.wikipedia.org/wiki/Triple_product

   The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. Geometric interpretation

7. Solving quadratic equations with continued fractions - Wikipedia

   en.wikipedia.org/wiki/Solving_quadratic...

   If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is positive the equation has two real roots, and the continued fraction converges to the larger (in absolute value) of these. The rate of convergence depends on the absolute value of the ratio between the two roots: the farther that ...