Order of rotational symmetry of a square

Step by step

The question

Question: what is the order of rotational symmetry of a square?

1 Mark a corner

Put a dot on one corner, so we can follow it.

Then turn the shape about its center.

2 Turn and count

After a quarter turn, it fits on itself again.

That is 1.

After a half turn, it fits on itself again.

That is 2.

After three quarter turns, it fits on itself again.

That is 3.

One more turn: the dot is back at the start.

That is 4.

3 The order

It fits 4 times in one full turn.

So the order is 4.

Careful!

The start and the full turn are the same place.

Count it once.

4 Check

Let's check.

One full turn is 360 degrees.

Shared by 4, each turn is 90°.

4 turns of 90 degrees make 360 degrees: one full turn.

Right!

Let's look back.

First: mark a corner.

Then: turn and count.

Then: the order.

Last: check.