Symmetry (Advanced)

We first learn about Symmetry in Geometry but Symmetry has a deeper and even more beautiful meaning

Symmetry means that a property does not change after a transformation

Imagine a long straight road: it has symmetry!

The symmetry is your position along the road. You can travel up and down the road and it stays the same.

A circle has symmetry: it's rotation.

And there is an amazing fact in Phyics: a symmetry has a matching conservation property.

• Translation symmetry leads to conservation of momentum
• Rotation symmetry leads to angular momentum
• Time symmetry leads to energy conservation
• etc

We have the genius Emily Noether to thank for this.