Spherical Triangles

When angles add up to more than 180°

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

• Triangles made of great-circle arcs have angle sums above 180°.
• Girard's theorem: area $= E R^2$, where $E$ is the spherical excess.
• Small triangles are nearly flat; the excess grows with area.

Steps

1. Three right angles
2. Girard’s theorem
3. A tenth of the world
4. Find the excess
5. A lune
6. How big for one degree?