The Shape of Space

Flat, closed or open

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

• Angle sums of triangles reveal curvature: more than 180° on a sphere, less on a saddle.
• CMB spots about 1° across show space is flat to within 0.4%.
• Flat space can still be finite, if it wraps around.

Steps

1. Triangles tell curvature
2. A triangle on a sphere
3. Measuring the Earth
4. A triangle across the universe
5. A surveyor’s triangle
6. Flat but finite?