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A number which is simultaneously octagonal and hexagonal. Let O_n denote the nth octagonal number and H_m the mth hexagonal number, then a number which is both octagonal and ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth ...

R(p,tau)=int_(-infty)^inftyint_(-infty)^inftyf(x,y)delta[y-(tau+px)]dydx, (1) where f(x,y)={1 for x,y in [-a,a]; 0 otherwise (2) and ...

Given a straight segment of track of length l, add a small segment Deltal so that the track bows into a circular arc. Find the maximum displacement d of the bowed track. The ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

If the coefficients of the polynomial d_nx^n+d_(n-1)x^(n-1)+...+d_0=0 (1) are specified to be integers, then rational roots must have a numerator which is a factor of d_0 and ...

A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems ...