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Rotations and Rotational Symmetry
Another type of symmetry is
rotational
symmetry.
Rotational symmetry results from the transformation called
rotation.
Rotation is the turning of a shape around a
center point called the
center of
rotation.
The distance to the center of rotation is kept constant. The
amount of turning called the
angle of
rotation
and is measured
in degrees.
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A simple rotation of a point (red) to form
another point
(blue). Notice that the distances from the
points to the
center of rotation remain the same.
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Here are two examples
of rotations applied to entire shapes, not just a single point.
The original shape together with its rotated copies is said to
have rotational symmetry.
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Here are two examples of rotation. On the
left, the "P" is being turned around the red
dot 60 degrees each time. On the right, the
polygon is being turned around the red dot
90 degrees each time.
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Finally,
what does it mean for a tessellation to have rotational
symmetry? If we can perform a rotation to a tessellation that
such that the result is the same as the original tessellation,
then the tessellation has rotational symmetry.
An example is as follows:
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This tessellation has rotational symmetry.
After rotation around the red point through
a certain number of degrees (60 to be
exact), you find that the copy exactly
matches the original.
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Real examples of rotational symmetry:
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Examples of Different Rotational Symmetry Order
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Order |
Example Shape |
Artwork |
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(using
Symmetry Artist) |
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... and there is also Order 5, 6, 7, and ... |
|
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 |
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... and then there is Order 9, 10, and so on ... |
Real World Examples
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A Dartboard has Rotational Symmetry of Order 10 |
The US Bronze Star Medal has Order 5 |
The London Eye has Order ... oops, I lost count! |
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