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Let a_n and b_n be the perimeters of the circumscribed and inscribed n-gon and a_(2n) and b_(2n) the perimeters of the circumscribed and inscribed 2n-gon. Then a_(2n) = ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by ...

Backgammon is a board game played by two players. The backgammon board is divided into four sections of six triangular regions on which pieces may be placed. Brown and white ...

Bessel's correction is the factor (N-1)/N in the relationship between the variance sigma and the expectation values of the sample variance, <s^2>=(N-1)/Nsigma^2, (1) where ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

A bounded operator T:V->W between two Banach spaces satisfies the inequality ||Tv||<=C||v||, (1) where C is a constant independent of the choice of v in V. The inequality is ...

A quadrilateral whose consecutive sides have the lengths a_1b_3, a_3b_2, a_2b_3, a_3b_1, where a_1^2+a_2^2=a_3^2 (1) and b_1^2+b_2^2=b_3^2. (2) Brahmagupta's trapezium is a ...

A Tschirnhausen transformation can be used to take a general quintic equation to the form x^5-x-a=0, where a may be complex.

Consider a quadratic equation x^2-sx+p=0 where s and p denote signed lengths. The circle which has the points A=(0,1) and B=(s,p) as a diameter is then called the Carlyle ...