Trisecting a Line Segment (with world record efficiency!)

Instructor's Guide

The immediate goal of this module is to discover the shortest way to trisect a line segment.  The bigger goal invites students to compare and contrast a variety of possible geometric constructions.  The module begins with a trisection using four lines and two circles, then shows how to construct one with three lines and two circles, then with two lines and three circles, then finally with four circles.  We next consider constructions using only circles (Mohr-Mascheroni) and finally using only lines (Poncelet-Steiner).  Proofs are given for each construction.  The Maple files showing the minimality of various constructions are meant for the connoisseur and not your students. 

Some ideas for using this module:

Annotated References  

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