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Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...

Suppose a line L^' meets sidelines BC, CA, and AB in points A^', B^', and C^', respectively. Let A^('') be the reflection of A^' about the midpoint of segment BC, and ...

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are isarithm, isopleth, and contour line. A plot of several ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

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 ...