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The van Aubel line is the line in the plane of a reference triangle that connects the orthocenter H and symmedian point K, and symmedian point of the orthic triangle. The ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

The set of roots of a polynomial f(x,y,z)=0. An algebraic surface is said to be of degree n=max(i+j+k), where n is the maximum sum of powers of all terms ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract logic theory. Analysis is the ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...