[br]Rotational symmetry is all about turning shapes around a pivot point.[br][br]Imagine you have a little windmill placed in the garden. If the mill is spinning around its center you might notice something interesting. After it was rotated, the shape looks exactly the same as it did before it was spinned by the wind.

This idea of turning a shape [u]and having it look the same[/u] is what we call [b]rotational symmetry[/b]. The point around which you turn the figure is called the [b]pivot point [/b]or the[b] center of rotation.[br][br][/b]When we try the calculate the smallest angle of rotation, we're trying to find the smallest angle that we can turn the shape so that it looks exactly the same as it did before. To do this, we need to think about how many times we can turn the shape before it repeats itself.[br]You can find the smallest number of degrees over which you can turn the windmill as follows:[list][*]turning a [b]full circle[/b] is[b] [math]360^\circ[/math][br][/b][/*][*]the windmill will turn a full circle in[b] 8 steps[/b][/*][*][b]per step[/b] it is[b] [math]360^{\circ}\div8=45^{\circ}[/math].[/b][/*][*]Therefore the [b]smallest angle of rotation is [math]45^\circ[/math][/b][/*][/list][br]When you turn the mill over [math]90^\circ,135^\circ,180^\circ,225^\circ,270^\circ,315^\circ[/math]and [math]360^\circ[/math]the mill will also appear unchanged.[br][br][br]another example: let's take a square. If we turn it 90 degrees (a quarter turn), it looks the same. If we turn it 180 degrees (a half turn), it still looks the same. But if we turn it 45 degrees, it doesn't look the same. So, the smallest angle of rotation for a square is 90 degrees.[br][br]If the smallest angle of rotatation is 360[math]^\circ[/math], then it does not have rotational symmetry. [br][br]Point symmetry is a special case of rotational symmetry in which the smallest angle of rotation is 180[math]^\circ[/math].[br][br][br][b]Difference between line symmetry, rotational symmetry and point symmetry:[/b][br][table][tr][td]Line symmetry[br]____________________________________[/td][td]Rotational symmetry[br]__________________________________________[/td][td]Point symmetry[br]__________________________________________[/td][/tr][tr][td]You fold figures that have [br]line symmetry [b]over a line[/b][/td][td]You turn figures that have [br]rotational symmetry [b]around a point[/b][/td][td]You turn figures that have [br]rotational symmetry [b]around a point with an angle of rotation of 180[math]^\circ[/math][/b][/td][/tr][/table]