Butterfly theorem

The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows:^[1]^{: p. 78}

For the "butterfly lemma" of group theory, see Zassenhaus lemma.

Let $M$ be the midpoint of a chord $PQ$ of a circle, through which two other chords $AB$ and $CD$ are drawn; $AD$ and $BC$ intersect chord $PQ$ at $X$ and $Y$ correspondingly. Then $M$ is the midpoint of $XY$ .

History[edit]

Proving the butterfly theorem was posed as a problem by William Wallace in The Gentleman's Mathematical Companion (1803). Three solutions were published in 1804, and in 1805 Sir William Herschel posed the question again in a letter to Wallace. Rev. Thomas Scurr asked the same question again in 1814 in the Gentleman's Diary or Mathematical Repository.^[4]

at cut-the-knot

The Butterfly Theorem

at cut-the-knot

A Better Butterfly Theorem

at PlanetMath

Proof of Butterfly Theorem

by Jay Warendorff, the Wolfram Demonstrations Project.

The Butterfly Theorem

"Butterfly Theorem". MathWorld.

Butterfly theorem

History[edit]

The Butterfly Theorem

A Better Butterfly Theorem

Proof of Butterfly Theorem

The Butterfly Theorem

Weisstein, Eric W.