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Successive points dividing a golden rectangle into squares lie on a logarithmic spiral (Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the golden spiral. ...

A near noble number is a real number 0<nu<1 whose continued fraction is periodic, and the periodic sequence of terms is composed of a string of p-1 1s followed by an integer ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

A number is squareful, also called nonsquarefree, if it contains at least one square in its prime factorization. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS ...

Binet's formula is an equation which gives the nth Fibonacci number as a difference of positive and negative nth powers of the golden ratio phi. It can be written as F_n = ...

Let f(x) be a monic polynomial of degree d with discriminant Delta. Then an odd integer n with (n,f(0)Delta)=1 is called a Frobenius pseudoprime with respect to f(x) if it ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...