Skolelaboratoriet Logo

Skolelaboratoriet is a department that is housed on the same floor as Matematikksenteret where I work. My first day on the job I was pleased to see their logo:

 

Can you see what is special about it?

 

It show a dissection of a square into an equilateral triangle. The white piece in the middle stays in place and is common to both the square and equilateral triangle. The three upper pieces which are part of the square are moved below, each with a 180° rotation, to create the equilateral triangle on the bottom. I've never tried to work out the angles and lengths involved to accomplish such a dissection, but it looks like a nice little problem. I'll try to remember to think about this next time I have a long flight.

The dissection is even a little better than a simple cut-and-rearrange: the pieces can be hinged so that one form turns inside out to become the other.

George Hart presents a coffee table that performs this trick:

http://blog.makezine.com/2011/04/04/math-monday-mathematical-coffee-table/