A shape has[i] [b]rotational symmetry[/b][/i] when it looks the same after some rotation by a partial turn about its center. [br]The [i][b]order [/b][/i]of the rotational symmetry is the number of times a shape can “fit into itself” when it is rotated.[br][br]Let's explore the order of rotational symmetry of some regular polygons! [br][br]Use the [color=#6aa84f][b][i]sides[/i] [/b][/color]slider to select the number of sides of the polygon, then rotate the polygon using the [color=#674ea7][i][b]rotate[/b][/i] [/color]slider, until the rotated shape overlaps the original one exactly. [br][br]Complete the full rotation of your polygon, and [b][i]count [/i][/b]the number of times that it overlapped the original one.
How many times has your polygon overlapped the original one, after a full rotation of 360°?[br][br]Can you relate the number of sides of the polygon and its order of rotational symmetry?
The polygon overlapped the original one [b][i]as many times as the number of its sides[/i][/b].[br][br]Thus for example a regular triangle has an order of rotational symmetry of 3, a regular hexagon has an order of rotational symmetry of 6, and so on.
Now imagine rotating a circle about its center, and consider the definition of rotational symmetry.[br][br]What is the order of rotational symmetry for a circle?
We can rotate a circle about its center, and its shape will always remain identical[br][br]Thus, [b][i]the order of rotational symmetry for a circle is infinite[/i][/b].