Time Dilation = 1/squareroot of 1-v^2/c^2 but why? How do you get to that conclusion? I know you use Pythagoras'theorem and my current understand goes like this:

vt^2+ct^2=cT^2

then you take the square root of Ct^2 and from there I think you divide by c to get the time dilation but I'm not sure. And if this is correct what steps do you take to get to the formula used now