Geometric Constructions using a Compass and Marked Straightedge

Geometric Constructions using a Compass and Marked Straightedge
 
Abstract: It is impossible to trisect an arbitrary angle, to double the cube, and to construct every regular polygon with a compass and straightedge. But Archimedes showed that if a straightedge is marked so it is able to make one measurement, then, by using a technique called a neusis construction, it is possible to trisect any angle. It is also possible to double the cube and to construct additional regular polygons. In this talk, we look at the history of the neusis construction from Archimedes to the present day, and we discuss what additional geometric constructions are possible using these tools.
 
Directions:  Villanova University is located on Route 30, Lancaster Avenue, just east of I-476.  If you drive to the meeting, enter Villanova by the main gate on Ithan Avenue. By order of the Parking Office all parking is now in the Saint Augustine Center lot, newly refurbished to a multistory structure. The Saint Augustine Center is attached to the lot, and Room 300 is on the third floor. You can get in touch with me (Alan Gluchoff) at 267-637-1759 if you need help.
 
Public Transportation: Take SEPTA’s Paoli-Thorndale train to the Villanova station. If outbound from center city go down through the tunnel to the inbound side. From the inbound platform go up the stairs and proceed to the left.  The second building you encounter is the SAC; entry is through the parking lot or the front entrance.