ABSTRACT

Summary Students are shown a paper folding routine that seems to trisect any acute angle. Is it for real? A proof or refutation is needed.

Content The heart of this activity is straightforward geometry. However, the implications from the fact that origami can trisect angles are, for one, that origami is a more powerful construction method than straightedge and compass. This means that the field of origami constructible numbers is larger than the smallest subfield of C closed under square roots. (See the previous activity for a lead-in to this.)

This activity can be especially captivating in the context of a discussion on the classic Greek problems of trisecting an angle and doubling the cube.