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A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...

int_0^(pi/2)cos^nxdx = int_0^(pi/2)sin^nxdx (1) = (sqrt(pi)Gamma(1/2(n+1)))/(nGamma(1/2n)) (2) = ((n-1)!!)/(n!!){1/2pi for n=2, 4, ...; 1 for n=3, 5, ..., (3) where Gamma(n) ...

If two curves of the same curve genus >1 are in rational correspondence, then that correspondence is birational.

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been ...

A zero tensor is a tensor of any rank and with any pattern of covariant and contravariant indices all of whose components are equal to 0 (Weinberg 1972, p. 38).

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

A triangle in which all three angles are acute angles. A triangle which is neither acute nor a right triangle (i.e., it has an obtuse angle) is called an obtuse triangle. ...

The Archimedean solids in general have many stellations. Examples of Archimedean solid stellations include the dodecadodecahedron and great icosidodecahedron. The following ...