Points at Infinity

A plane where any two lines meet

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The projective plane adds points at infinity where parallel lines meet.
• Any two lines meet in exactly one point; points and lines are dual.
• Circles, ellipses, parabolas and hyperbolas are all projectively the same conic.

Steps

1. The projective plane
2. Running off to infinity
3. One conic to rule them all
4. The smallest projective plane
5. A bigger finite plane
6. Desargues’ theorem