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In 1750, Benjamin Franklin constructed the above 8×8 semimagic square having magic constant 260. Any half-row or half-column in this square totals 130, and the four corners ...

When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

The Frobenius number is the largest value b for which the Frobenius equation a_1x_1+a_2x_2+...+a_nx_n=b, (1) has no solution, where the a_i are positive integers, b is an ...

A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

Gauss's forward formula is f_p=f_0+pdelta_(1/2)+G_2delta_0^2+G_3delta_(1/2)^3+G_4delta_0^4+G_5delta_(1/2)^5+..., (1) for p in [0,1], where delta is the central difference and ...

If u_n>0 and given B(n) a bounded function of n as n->infty, express the ratio of successive terms as |(u_n)/(u_(n+1))|=1+h/n+(B(n))/(n^r) for r>1. The series converges for ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...

The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos ...