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Let s_i be the sum of the products of distinct polynomial roots r_j of the polynomial equation of degree n a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the roots are taken ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

The Weierstrass zeta function zeta(z;g_2,g_3) is the quasiperiodic function defined by (dzeta(z;g_2,g_3))/(dz)=-P(z;g_2,g_3), (1) where P(z;g_2,g_3) is the Weierstrass ...

The Wythoff array is an interspersion array that can be constructed by beginning with the Fibonacci numbers {F_2,F_3,F_4,F_5,...} in the first row and then building up ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...