How do I prove that different unit speed reparametrisations of the same curve give same curvature?
I tried to consider two unit reparametrisations $\gamma_1(s)$ and $\gamma_2(u)$ where $u = \pm s + c$ where s is the arc length of $\gamma_1$ and c in some constant and then tried to show that $\dot\gamma_1 = \dot\gamma_2$. But I couldn't show it and I'm not even sure if it is the right condition. Any help in proving this would be appreciated.