A lot of people have indulged in the exercise of trying to catalog the exact set of basic operations that paper-folding permits. A consensus set are the so-called Huzita-Hatori axioms, although ultimately the choice of what's "allowed" is a matter of taste, as in any axiom system. (Note that Dr. Huzita chose to romanize his name using the "Kunrei-shiki" system, rather than the Hepburn system more familiar to Westerners. The situation a fairly nuanced, but let's just say his name is pronounced "Fujita".) The geometry induced by the HH axioms is indeed more powerful than compass-and-straightedge, and permits angle trisection, and, more generally, finding the real roots of any cubic equation. On Mon, Dec 17, 2018 at 4:26 PM James Propp <jamespropp@gmail.com> wrote:

In his video "How to Make a Paper Snowflake" ( https://www.youtube.com/watch?v=BIiEsIDenTk&feature=youtu.be ) Matt Parker shows how to trisect a 180 degree angle by pulling a fold in a constrained fashion until it meets a certain point.

It seems to me that this method should allow one to construct some angles that can't be trisected with straightedge and compass. And I suspect it's one of the already-studied construction methods that go beyond straightedge and compass.

Do any of you know anything about this?

Thanks,

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun