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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 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 ...

The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the ...

The integer sequence defined by the recurrence relation P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=P(1)=P(2)=1. This is the same recurrence relation as for the ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...