Duplicating the cube and other notes on constructions in the hyperbolic plane

The Euclidean classical problem ofDuplicating the Cube is investigated for the first time inhyperbolic geometry, and its partial solution presented. The other two associated problems ofTrisecting an Angle andSquaring the Circle in the hyperbolic plane were solved classically, but a few additions to these solutions are presented, along with some miscellaneous notes about straightedge and compass constructions in the hyperbolic plane.A preliminary version of this paper was presented at the MAA Undergraduate Student Paper Session, August 1987, Salt Lake City AMS/MAA Joint Meetings. Financial support was provided by a J.W.T. Youngs Undergraduate Award in Mathematics (UC Santa Cruz), and UCSD.