MATHEMATICAL ORIGAMI: ANOTHER VIEW OF ALHAZEN'S OPTICAL PROBLEM Summary: MATHEMATICAL ORIGAMI: ANOTHER VIEW OF ALHAZEN'S OPTICAL PROBLEM Roger C. Alperin 1. Fields and Constructions We can solve some elementary problems from geometry using origami foldings. Below are the axioms which guide the allowable constructible folds and points in C, the field of complex numbers, starting from the labelled points 0 and 1 (see [1] for more details and references) . (1) The line connecting two constructible points can be folded. (2) The point of coincidence of two fold lines is a constructible point. (3) The perpendicular bisector of the segment connecting two constructible points can be folded. (4) The line bisecting any given constructed angle can be folded. (5) Given a fold line l and constructed points P, Q, then whenever pos- sible, the line through Q, which reflects P onto l, can be folded. (6) Given fold lines l, m and constructed points P, Q, then whenever possible, any line which simultaneously reflects P onto l and Q onto m, can be folded. The first three are the Thalian constructions which ensure that we have a field after we have a non-real complex number z. Some proper- Collections: Mathematics