Quadratic equations in Ancient Egypt. From my reading, I understand that the Ancient Egyptians had some knowledge of solving quadratic equations.  Is it known what applications they used this knowledge for, or whether they were studying these in a "pure maths" sense?  Can anyone suggest any good references in this area?

I am unaware of quadratic problems in ancient Egypt (except for a pure quadratic "equation" in the Berlin papyrus, which can be solved by the technique of false position). The Babylonians, on the other hand, were familiar with techniques for solving such problems. A very good source concerning their methods is Jens Hoyrup's book Algebra in cuneiform which is freely available here.
Although they used these problems in the education of scribes and surveyors, the vast majority of these problems belong to what you call "pure maths".
