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The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

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 ...

If isosceles triangles with apex angles 2kpi/n are erected on the sides of an arbitrary n-gon A_0, and if this process is repeated with the n-gon A_1 formed by the free ...

Given the center of a circle, divide the circle into four equal arcs using a compass alone (a Mascheroni construction).

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

The first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances ...

The converse of Fisher's theorem.

There are several theorems that generally are known by the generic name "Pappus's Theorem." They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

The reciprocity theorem for x^8=q (mod p).