This article is within the scope of WikiProject Greece, a collaborative effort to improve the coverage of Greece on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
I have checked the references cited in this article and I can find no evidence that "Hippocrates wanted to solve the classic problem of squaring the circle, i.e. constructing a square by means of straightedge and compass, having the same area as a given circle." There was a misinterpretation that he had in fact squared the circle, but this was incorrect, and Hippocrates knew that he had not squared the circle. Check Heath's "A History of Greek Mathematics" Volume 1, page 221
A Response: Page 183 of Heath vol. 1 relates an annecdote about Hippocrates trying to square the circle. Hippocrates is credited here as one of the first authors of an Elements text, predating Euclid. He is also credit (page 202) with showing that the area of circles is proportional to the squares of their diameters. While page 221 does express Heath's opinion that Hippocrates was not deluded by his successes into believing the problem was solved, it seems he did make 2 really interesting contributions to our understanding of the problem.
The Lune of Hippocrates is a special case of Lunes of Alhazen. -- Fauzan✆ talk✉ email 06:11, 15 January 2014 (UTC)
And those are a special case of the lunes found by Chebataryov. But most of this article is about the Lune of Hippocrates; those other ones are mentioned only briefly in a generalizations section. So I think the current title is the right one. —David Eppstein (talk) 13:17, 15 January 2014 (UTC)