Hi Nothing to do with teaching unless you've very advanced students. Following puzzle: If SQR(2) is an irrational number = 1.414........(ad infinitum), is it possible for a right angled triangle to even exist theoretically. Consider RA Triangle with two sides of 1 and 1 , then hypotenuse = SQR(2) In a theoretical world of perfect lines and angles, would this mean that any hypotenuse will ALWAYS be either too short or too long to fit a perfect figure? How do you specify the length of the hypotenuse to the drawer? When should he stop drawing the line? Remember, we're talking about a perfect diagram with lines of zero width and perfect angles. My solution? I'm going to open a bottle of beer. ) Any thoughts?