Butterfly theorem formula: XM=MY. 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.

Plane geometry refers to geometry constructed according to Euclid's Elements of Geometry. Also known as Euclidean geometry. Plane geometry studies the geometric structure and measurement properties (area, length, angle and position relationship) of straight lines and quadratic curves (that is, conic curves, that is, ellipses, hyperbolas and parabolas) on a plane. Plane geometry adopts axiomatic method, which is of great significance in the history of mathematical thought.