Does the curve $(t^2,t^2)$ has singularity at $t=0$?

Question

Suppose the curve $\gamma(t)=(t^2,t^2),t\in (-\infty,+\infty)$,then its speed is $\dot \gamma(t)=(2t,2t)$.The speed vanishes at $t=0$.So,the curve is not regular i.e.the curve is singular at $t=0$.I want to know what is causing this singularity?Is this singularity removable?

Answer 1

The concept of removable singularity arises in the context of complex analysis. We say that an isolated singularity $z_0$ of an analytic function $f$ is a removable singularity when we can extend $f$ to an analytic function whose domain is $D_f\cup\{z_0\}$.

But here, no such concept exists. We just say that $0$ is a singular point of $\gamma$.