symmetry

SYMMETRY

Symmetry.

The more it changes, the more it stays the same.

Now that’s a wonder!

EPISODE 1: Symmetry as a transformation

A symmetry is a transformation …

that leaves an object looking unchanged.

EPISODE 2: Rotation symmetries of the square

How many rotation symmetries does a square have?

EPISODE 3: Symmetry as a permutation

A zero rotation, or 1234

When we label the vertices of the square with 1, 2, 3, and 4 dots, we can find permutations that are equivalent to symmetries.

A permutation is an arrangement of a set or subset of objects.

Here are the 4 rotation symmetries of the square as permutations.

EPISODE 4: Reflection symmetries of the square

Rotation symmetries stay as a group.

Reflection symmetries like to meet new “friends” when they transform one another.

EPISODE 5: Bumper symmetries

Symmetries as bumper cars.

What happens when you imagine the 4 rotation symmetries of the square as bumper cars, where they transform one another as they bump?

Grades 2/3 students used sticky notes to simulate this.

EPISODE 6: Symmetry and coding, part 1

… coming soon

EPISODE 7: Symmetry and coding, part 2

… coming soon

EPISODE 8: Symmetry and group theory

… coming soon