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Math · Intermediate

Compass & Straightedge

With nothing but a compass and an unmarked ruler, the ancient Greeks constructed triangles, bisectors, hexagons and pentagons. Three puzzles defeated them for over 2,000 years. Learn the constructions, follow the teenage Gauss to the 17-sided polygon, and see how algebra finally proved that some constructions are impossible.

9 lessons~50 min0/9 complete
1

The Rules of the Game

Two tools and the first constructions.

  1. Euclid’s ToolsCircles, lines and an equilateral triangle
  2. Cutting in HalfMidpoints and bisectors
  3. Perpendiculars & ParallelsRight angles and parallel lines
  4. Tangents to a CircleThales to the rescue
2

Regular Polygons

Which shapes can be built?

  1. Hexagons & PentagonsStepping around a circle
  2. Squares & OctagonsDoubling from four
  3. Gauss’s 17-gonA teenager’s discovery
3

The Impossible Three

Problems that can never be solved.

  1. Constructible NumbersLengths built from square roots
  2. Three Famous ProblemsDoubling, trisecting and squaring