Constructions on the Sphere

The geometric constructions we learn in high school can be thought of as a one-player game of skill where the goal is to produce some planar geometric figure from a set of givens.  The challenge is to do so using only two tools, a straightedge and compass.  For example, we can use these tools to bisect a given line segment or a given angle, or to construct an equilateral triangle from a given segment.  The game is as old as the history of demonstrative mathematics, and as such, has been played for over two millennia.  After reviewing some basic constructions in the plane, we add the twist of playing the game on the surface of a sphere and consider the following questions:  What is a spherical straightedge?  Is it possible to replicate the constructions from the plane?  Does our new surface allow for new constructions? 

We encourage mathematics majors to attend.