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The pentanacci constant is the limiting ratio of adjacent pentanacci numbers. It is the algebraic number P = (x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.96594823... (2) (OEIS A103814), ...

The base-60 notational system for representing real numbers. A base-60 number system was used by the Babylonians and is preserved in the modern measurement of time (hours, ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known ...

The algebraics, sometimes denoted A (Derbyshire 2004, p. 173), are the set of algebraic numbers. The set of algebraic numbers is implemented in the Wolfram Language as ...

Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} is complete, even if one is restricted to subsequences in which no two consecutive ...

Let t be a nonnegative integer and let x_1, ..., x_t be nonzero elements of Z_p which are not necessarily distinct. Then the number of elements of Z_p that can be written as ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

The sum of powers of even divisors of a number. It is the analog of the divisor function for even divisors only and is written sigma_k^((e))(n). It is given simply in terms ...

Let the residue from Pépin's theorem be R_n=3^((F_n-1)/2) (mod F_n), where F_n is a Fermat number. Selfridge and Hurwitz use R_n (mod 2^(35)-1,2^(36),2^(36)-1). A ...