Double Mean Proportionals
Hipprocrate of Chios, a famous Greek mathematician did a lot of influential work on the three classical problems. He considered Delian problem in a more general form - the problem of constructing the so-called "double mean proportionals": Given two lengths and , find the lengths and such that
By simple algebra, it is easy to see that if and , then
How Hipprocrate came up with such idea? One possible explanation is that he was inspired by the following well-known result at his time: The following two problems are equivalent:
- Given a square, construct a square whose ratio between their areas equals a given ratio .
- Given and , construct the "mean proportional" between them i.e. a number such that .