- #1

MathematicalPhysicist

Gold Member

- 4,168

- 161

## Main Question or Discussion Point

I need to show that every isometry in the plane is a composition of at most three reflections.

Now every isometry in the plane is one of the four:

1.translation.

2.rotation.

3.reflection.

4.glide.

now obviously refelction is itself.

now for translation i showed with a picture that we need only two reflections.

for rotation we need something like 3 reflections, and also for glide, which answers another question is it possible for glide to be a composition of just two reflection, i don't think so, but don't see how to show this.

Is any of what i wrote make sense?

thanks in advance.

Now every isometry in the plane is one of the four:

1.translation.

2.rotation.

3.reflection.

4.glide.

now obviously refelction is itself.

now for translation i showed with a picture that we need only two reflections.

for rotation we need something like 3 reflections, and also for glide, which answers another question is it possible for glide to be a composition of just two reflection, i don't think so, but don't see how to show this.

Is any of what i wrote make sense?

thanks in advance.