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The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...

A surface generated by the parametric equations x(u,v) = ucosv (1) y(u,v) = usinv (2) z(u,v) = vcosu. (3) The above image uses u in [-4,4] and v in [0,6.25]. The coefficients ...

A number which is simultaneously octagonal and triangular. Let O_n denote the nth octagonal number and T_m the mth triangular number, then a number which is both octagonal ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

A cyclic number is an (n-1)-digit integer that, when multiplied by 1, 2, 3, ..., n-1, produces the same digits in a different order. Cyclic numbers are generated by the full ...

A (-1,1)-matrix is a matrix whose elements consist only of the numbers -1 or 1. For an n×n (-1,1)-matrix, the largest possible determinants (Hadamard's maximum determinant ...

Feynman (1997, p. 116) noticed the curious fact that the decimal expansion 1/(243)=0.004115226337448559... (1) repeats pairs of the digits 0, 1, 2, 3, ... separated by the ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

A centered polygonal number consisting of a central dot with four dots around it, and then additional dots in the gaps between adjacent dots. The general term is n^2+(n+1)^2, ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...