MASC 380 Assignment #4

1. Show that the following construction for trisecting an angle using a compass and a ruler with two marks (a distance of r apart) works.

Given that angle AOB = theta, draw a circle with centre O and radius r. Suppose this circle intersects OA at X and the line extending BO past O at Y. Slide the ruler around until its edge runs through X, one mark is on the line extending OY past Y, and the other mark lies on the circle. Let D be the point on the line where the first mark is and E be the point on the circle where the second mark is. Then angle EDY = theta/3. [5]

2. Describe some of the tools besides a compass and an unmarked straightedge that Greek and Hellenistic geometers experimented with. What constructions did these make possible that cannot be accomplished with a compass and straightedge alone? [5]

Department of Mathematics

Trent University