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The elliptic modulus k is a quantity used in elliptic integrals and elliptic functions defined to be k=sqrt(m), where m is the parameter. An elliptic integral is written ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...

A curious approximation to the Feigenbaum constant delta is given by pi+tan^(-1)(e^pi)=4.669201932..., (1) where e^pi is Gelfond's constant, which is good to 6 digits to the ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player ...

The great icosidodecahedron, not to be confused with the great icosahedron or great icosicosidodecahedron, is the uniform polyhedron with Maeder index 54 (Maeder 1997), ...

The harmonic mean H(x_1,...,x_n) of n numbers x_i (where i=1, ..., n) is the number H defined by 1/H=1/nsum_(i=1)^n1/(x_i). (1) The harmonic mean of a list of numbers may be ...

A transformation of the form w=f(z)=(az+b)/(cz+d), (1) where a, b, c, d in C and ad-bc!=0, (2) is a conformal mapping called a linear fractional transformation. The ...

The modular equation of degree n gives an algebraic connection of the form (K^'(l))/(K(l))=n(K^'(k))/(K(k)) (1) between the transcendental complete elliptic integrals of the ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...