Four conclusions of butterfly model

Butterfly model is the most basic plane geometry algorithm model, and its four conclusions are as follows:

1, similar to a graph, the area ratio is equal to the square of the contrast ratio, that is, s1:S2 = a 2/b 2.

2、S 1:S2:S3:S4= a？ :b？ :ab:ab .

3.S 1×S2=S3×S4 (derived from S 1/S3=S4/S2).

4. Ao: Bo =(S 1+S3):(S2+S4).

The origin of butterfly theorem;

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.

Using butterfly model to find the equation and eccentricity of conic curve is a common method in plane geometry examination questions, which is very helpful for students to develop creative thinking.