MATH 2741 Geometric Constructions

MATH 2741 is about geometric constructions, which mean drawing geometric figures using specific drawing tools like straightedge, compass and so on.  This classical topic in geometry is important because

• the foundation of geometry is mostly inspired by what we can do with all these drawing tools, and
• it involves a lot of beautiful mathematics that shows the interplay between geometry and algebra.

Click "Play" to see a typical geometric construction

The following is the brief outline of what you are going to learn in this course:

• A brief history of geometry - we will go through the history and development of ancient geometry and the origin of geometric constructions.
• Euclidean constructions - we will investigate geometric constructions using straightedge and compass.
• Constructibility and the three classical problems - with the help of algebra, we will find out exactly what kind of geometric figures can be constructed by straightedge and compass.  The theory we will establish is closely related to the three classical problems in ancient geometry. 
• Compass-only constructions - we will investigate geometric constructions using compass alone and prove the famous Mohr-Mascheroni theorem.
• Straightedge-only constructions - we will investigate geometric constructions using straightedge alone and prove the Poncelet-Steiner theorem.
• Regular polygons - we will learn how to construct various regular polygons using straightedge and compass and Gauss' famous results on the constructibility of regular polygons.
• Quadrature (Optional) - we will learn how to "square" a polygon i.e. construct a square whose area equals the area of the polygon using straightedge and compass.  

Pre-requisite for MATH 2741

• MATH 1014 OR MATH 1018 OR MATH 1020 OR MATH 1024 OR AL Applied Mathematics / AL Pure Mathematics

The Format of this course

The format of this course is a bit different from other math courses - we adopt the "blended-learning" approach, which means that a large part of the course materials will be taught through Canvas, the new online learning platform.  Lectures in classroom are reserved for more in-depth learning and discussions, which consolidate and extend what you have already learned online.