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

Time Dilation = $1/\sqrt{ 1-v^2/c^2}$ 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

I know that time dilation and length contraction are "governed" by the Lorentz factor $$\gamma=\left(\sqrt{1-\frac{v^2}{c^2}}\right)^{-1}$$ But what is the intuition behind this (strange-looking) expression

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

Time Dilations = 1/squareroot of 1-v^2/c^2 but why?

I know that time dilation and length contraction are "governed" by the Lorentz factor $$\gamma=\left(\sqrt{1-\frac{v^2}{c^2}}\right)^{-1}$$ But what is the intuition behind this (strange-looking) expression