Outline
Geometric Constructions
This is an interactive course on geometric constructions, a fascinating topic that has been ignored by the mainstream mathematics education. It is all about 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.
- A little bit set theory
- High school geometry and algebra
Table of Contents
Euclidean Constructions
- Introduction
- Copy a Line Segment
- Bisect an Angle
- Construct an Equilateral Triangle
- Copy a Triangle
- Copy an Angle
- Construct a Perpendicular Bisector and Midpoint
- Construct a Perpendicular Line
- Construct a Parallel Line
- Construct a Point of Division
- Circumcircle of a Triangle
- Using Euclidean Compass
- Tangents of a Circle
- Inscribe a Circle in a Triangle
Constructibility
Three Classical Problems