Symmetry in Nature

Crystals, cubes and conservation laws

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

• Crystals fall into 230 space groups, and wallpaper patterns into 17.
• Noether: time symmetry → energy, space → momentum, rotation → angular momentum.
• Symmetry groups have predicted new particles.

Steps

1. Groups everywhere
2. Noether’s theorem
3. Match the symmetry
4. Every position
5. A snowflake’s turns
6. Particles from symmetry