Tag: Irrational number

A circle inscribing a pentagon
This is also from The IrrationalsĀ – though I had to ask for assistance over at Stack Exchange to get the right answer (as is so often the case the solution is reasonably obvious when you are presented with it). Anyway, the question is: given a regular pentagon (of sides with length of 10 units) which […]

The proof that frightened Pythagoras
I have been meaning to do this for a while … Pythagoras was said to be shocked by the proof that is an irrational number (i.e., that it cannot be represented as a ratio of two whole numbers). The proof (by contradiction) is a simple one. If is rational then and where and are the […]