Trying to understand velocity addition and time dilation

Question

I'm familiar with Einstein's formulae $V=\frac{u+v}{1+ \frac{uv}{c^2}}$ and $\Delta t'=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$, the former being velocity addition and the latter being time dilation. Each of these equations imply that you can't go faster than light; the former cannot exceed $c$, and the latter will give an imaginary number in the denominator if you try.

But why are these formulae true? I understand it numerically, but how would you explain this conceptually?

Answer 1

The key concept is: space-time is 4 dimensional Minkowski space, and not 3 dimensional Euclidean space with a universal time parameter for all.