The ancient Greeks struggled with the concept of a horn angle, the "angle" formed by the intersection of two curves. The only information I find in Mathworld is that horn angles are examples of non-Archimedean geometry. Where can I find out more about them? What work has been done on them, and what is the current state of knowledge on them?

Since they are part of non-Archimedean geometry, can they be understood using the hyperreal numbers or some other non-standard model of the first-order theory of real closed fields?

Any help would be greatly appreciated. Thank You in Advance.

andcertain radii, see e.g. "Foundations and fundamental concepts of mathematics" by Howard Whitley Eves, p. 107 (Problems). – M.G. Feb 22 '11 at 21:22