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Symmetry

[syn- together + metron measure]

Reflection Symmetry

The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry). It is easy to recognise, because one half is the reflection of the other half.

 

Here my dog "Flame" has her face made perfectly symmetrical with a bit of photo magic.

The white line down the center is the Line of Symmetry

 

The reflection in this lake also has symmetry, but in this case:

  • the Line of Symmetry is the horizon
  • it is not perfect symmetry, because the image is changed a little by the lake surface.

The Line of Symmetry does not have to be up-down or left-right, it can be in any direction. To learn more, go to Reflection Symmetry.

Rotational Symmetry

With Rotational Symmetry, the image is rotated (around a central point) so that it appears 2 or more times. How many times it appears is called the Order.

Here are some examples (they were made using Symmetry Artist, and you can try it yourself!)

Order Example Shape Artwork
... and there is Order 4, 5, etc ...

Point Symmetry

Point Symmetry is when every part has a matching part:

  • the same distance from the orgin
  • but in in the opposite direction.

(Note: this is the same as "Rotational Symmetry of Order 2" above)