Butterfly theorem is one of the most wonderful results in ancient Euclidean plane geometry. This proposition first appeared in 18 15 and was proved by W.G. Horner. The name "Butterfly Theorem" first appeared in the February issue of American Mathematical Monthly (1944), with the title like a butterfly.
There are countless proofs of this theorem, math lovers are still studying it, and there are various deformations in the exam. Butterfly theorem: let m be the midpoint of the inner chord PQ of a circle, and let m be the chords AB and CD. Let PQ where AD and BC intersect at points X and Y, then M is the midpoint of XY.
Proof of Butterfly Theorem This theorem is actually a special case of a theorem in projective geometry, which has many generalizations.
Development history:
This proposition first appeared in 18 15, pages 39-40 of the British magazine Diary of a Gentleman (P39-40). Interestingly, until 1972, people's proofs were not elementary and very complicated. ?
In the year when this article was published, W.G. Horner, a self-taught middle school math teacher in Britain (who invented Horner's polynomial equation approximate root method) gave the first proof, which was completely equal. Richard taylor gave another piece of evidence. ?
A book by m brand (1827) gives another early proof. The simplest proof method is projective geometry, which was given by J. Shikai of Britain in the first six sequels of Euclid's Elements of Geometry. There is only one sentence, using the cross ratio of the harness. ?
The name "Butterfly Theorem" first appeared in the February issue of the American Mathematical Monthly (1944) with the title of a butterfly. 198 1 year, Crossroads magazine published a relatively simple analytic geometry method used by K. Satyanarayana, which uses straight-line bundles and cone bundles. 1990, Zheng butterfly theorem appeared.