How_To_Be_Good_At_Math

GEOMETRY • ROTATIONAL SYMMETRY 259

Let’s see how many times this three-pointed

shape can fit into its outline. First, we rotate it

until the yellow tip reaches the next point.

Order of rotational symmetry

The number of times a shape can fit into its

outline during a full turn is called its order of

rotational symmetry.

Now we rotate the shape again so the

yellow tip moves to the next point.

Square

Rotational order: 4

Circle

Infinite number of

orders of rotation

Equilateral triangle

Rotational order: 3

Order of rotational symmetry

in 2D shapes

Here are the orders of rotational

symmetry for some common 2D shapes.

Centre of

rotational

symmetry

Symmetrical decoration

We often use rotational symmetry to make

decorative patterns. In Islamic art, reflective

and rotational symmetry are used to create

intricate patterns on tiles for mosques and

other buildings.

REAL WORLD MATHS

Follow the

coloured tip

as the shape

rotates

One more rotation and the yellow tip is back

where it started. This shape can fit onto itself

three times, so it has an order of rotational

symmetry of 3.

Hexagon

Rotational order: 6

Centre of

rotational

symmetry

Centre of

rotational

symmetry

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