The formula of butterfly theorem in primary schools is the proportional relation in any quadrilateral: S 1∶S2=S4∶S3 or S 1×S3=S2×S4, and the product of the upper and lower parts is equal to the product of the left and right parts. Butterfly theorem provides us with a way to understand the area problem of irregular quadrilateral.

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 Horner. The name "Butterfly Theorem" first appeared in the February issue of American Mathematical Monthly (1944), with the title like a butterfly.