Rules of Construction
- Author:
- Mathew Purser
What is a Construction?
A geometric construction is a precise drawing that historically only uses a compass and an unmarked straightedge (not a ruler) to solve geometric problems. Ideally, our paper is considered infinite, our lines are also infinitely long and we are not allowed to measure distances. You would be shocked the kinds of math you can do with just lines and circles.
We describe figures in our drawings in two different ways, given or constructed. A given figure is either provided at the start of the problem or arbitrarily picked while a constructed figure is drawn using the rules of construction and is considered precise.
Rules of Construction
Tool Rule: The only allowed tools are a compass and an unmarked straightedge
Point Rule: A point must either be given or constructed in the following ways:
1. The intersection of two lines
2. The intersection of a line and a circle
3. The intersection of two circles
Straightedge Rule: A straightedge can connect two points to construct a line, lines can be infinite
Compass Rule: A compass can construct a circle with a center and a point on its circumference. A compass can also copy a length
Tool Practice
Watch the animation below of me constructing a square with just these rules, feel free to use the applet below that to try and copy my steps. Don't worry if it seems overwhelming right now, we will work up to this.