impossible picture

it looks as if you can dissect a square into 5 pieces that will assemble to make 3 smaller squares...


use pythagoras and simple surd expressions to show that it doesn't work...

mistrusting diagrams

students probably need to know that diagrams aren't always trustworthy...

they can be asked to establish what is wrong with these diagrams that lead either to a missing area or an extra area after a dissection and a rearrangement

youtube clip

four variations on a theme:

what is wrong with these?

plus a chocolate generating device:

sometimes called the 'Tarski-Banach' paradox