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2. Generalized continued fraction - Wikipedia

   en.wikipedia.org/wiki/Generalized_continued_fraction

   A generalized continued fraction is an expression of the form. where the an ( n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction. The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas :

3. Rationalisation (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Rationalisation_(mathematics)

   In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that has x as its n th power).

4. Square root of 2 - Wikipedia

   en.wikipedia.org/wiki/Square_root_of_2

   The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number.

5. Approximations of π - Wikipedia

   en.wikipedia.org/wiki/Approximations_of_π

   The latter fraction is the best possible rational approximation of π using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's results surpass the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium.

6. Difference of two squares - Wikipedia

   en.wikipedia.org/wiki/Difference_of_two_squares

   This is used to get real denominators in complex fractions. Rationalising denominators. The difference of two squares can also be used in the rationalising of irrational denominators. This is a method for removing surds from expressions (or at least moving them), applying to division by some combinations involving square roots.

7. Cubic field - Wikipedia

   en.wikipedia.org/wiki/Cubic_field

   Adjoining a root of x 3 + x 2 − 2x − 1 to Q yields a cyclic cubic field, and hence a totally real cubic field. It has the smallest discriminant of all totally real cubic fields, namely 49. The field obtained by adjoining to Q a root of x 3 + x 2 − 3x − 1 is an example of a totally real cubic field that is not cyclic. Its discriminant is ...