On 3/5/2014 2:45 PM, Peter Percival wrote: > David Elkins wrote: >> I will try this one more time. Start with the length v2. > > You need to spell that "sqrt 2". > >> Now let's play imaginary game. Imagine that you picked up the length >> v2 with your hand and horizontal flipped the length. The v, which has >> a non-terminating decimal expansion would expand from both ends. > > Measure the diagonal of a unit square > > A-----B > | | > | | > C-----D > > from C to B, and from B to C, and the result is the same. Furthermore > and physical measurement will only yield finitely many of these digits: > > 1.4142135623730950488016887242097... > > Is that it? >
It's the principal root of x^2 = 2.
For isosceles right triangles, if the hypotenuse is rational then the edges are not and if the edges are rational the hypotenuse is not.
Then this would be for variation over the components of the proofs establishing 2^ -1/2 is not a ratio of integers.