Line and Rotation Symmetry

An object has a line of symmetry if it can be split into two halves which will fold or reflect exactly on top of each other across the line.

An object has rotation symmetry if it can be rotated about a point to look exactly the same in a new position.

You are going to use "Paint" to make images that have line and rotation symmetry.

Find a picture and cut a rectangle out of it. I've used a piece of a fossil ammonite but you could use a picture of your pet dog etc.
Paste (Ctrl v) this into a new "Paint" image several times.
As you do so, use the image flip/rotate tool to transform your rectangle. Stick the pieces together by cutting and pasting.
These images have one symmetry line.
This image has two-fold rotation symmetry.
This image has two lines of symmetry.
You can line your rectangles up next to each other so that you tile the plane.

Now make an A4 poster showing all these kinds of symmetry and a few examples of tiling patterns. Put a label under your images stating the kind of symmetry that they have. You could use a font with interesting symmetry to do this!

If you turn "Opaque" off and use the "Stretch and Skew" tools then you can do some really wierd things to your image.
The "Opaque" option is at the bottom of the menu.
This image tiles the plane with a unit cell that began with two lines of symmetry and order 2 rotational symmetry but has been skewed so that it now only has rotational symmetry.

Make another poster with your symmetry examples and tilings on it.
Are there shapes other than rectangles or parallelograms which will tile the plane?
What is the most symmetrical tiling that you can produce which will tile the plane?

If you rotate an image by 90 degrees and stick the results together then you can produce order 4 rotational symmetry.
You can stick blocks like this together to tile the plane. This symmetry of the block is not the same as the symmetry of the tiling.

Order three rotational symmetry is very difficult to produce in "Paint". You need to switch to a more powerful program such as "The GIMP", "Photoshop", Logo or Java.