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Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an ...

A right strophoid is the strophoid of a line L with pole O not on L and fixed point O^' being the point where the perpendicular from O to L cuts L is called a right ...

The 12-faced convex deltahedra also known as the Siamese dodecahedron, which is also Johnson solid J_(84). It is implemented in the Wolfram Language as ...

Define the sequence a_0=1, a_1=x, and a_n=(a_(n-2))/(1+a_(n-1)) (1) for n>=0. The first few values are a_2 = 1/(1+x) (2) a_3 = (x(1+x))/(2+x) (3) a_4 = ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

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

The quadrifolium is the 4-petalled rose curve having n=2. It has polar equation r=asin(2theta) (1) and Cartesian equation (x^2+y^2)^3=4a^2x^2y^2. (2) The area of the ...

A function defined for all positive integers, sometimes also called an arithmetic function (Nagell 1951, p. 26) or number theoretic function (Wilf 1994, p. 58).