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It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane ax+by+cz+d=0 (1) by defining the ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

The identity (xy)x^2=x(yx^2) satisfied by elements x and y in a Jordan algebra.

A quantity that is nonzero everywhere is said to be nonvanishing. For instance, the values of x^2+1 are nonvanishing for real x, while those of x^2 are not (since x^2 ...

The map x^' = x+1 (1) y^' = 2x+y+1, (2) which leaves the parabola x^('2)-y^'=(x+1)^2-(2x+y+1)=x^2-y (3) invariant.

A natural extension of the Riemann p-differential equation given by (d^2w)/(dx^2)+(gamma/x+delta/(x-1)+epsilon/(x-a))(dw)/(dx)+(alphabetax-q)/(x(x-1)(x-a))w=0 where ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

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 ...

Fischer's z-distribution is the general distribution defined by g(z)=(2n_1^(n_1/2)n_2^(n_2/2))/(B((n_1)/2,(n_2)/2))(e^(n_1z))/((n_1e^(2z)+n_2)^((n_1+n_2)/2)) (1) (Kenney and ...

The 12-faced convex deltahedra also known as the Siamese dodecahedron, which is also Johnson solid J_(84). It is implemented in the Wolfram Language as ...