Numerical Approach for Fermat's last theorem

This research focuses on the Numerical approach for Fermat's Last theorem. We can induce an Alternative form of Fermat's last theorem by using particular geometric mapping $\mathcal{M}$ on a Cartesian plane to a Torus. It transforms the Fermat's Last Theorem to finding a rational cross point between two parametric curves on the torus. In the end, this research shows the movement of the point, on the line $x^n+y^n=1$, has an acceleration phase transition near ($x,n$)=(0,2). Moreover, the studies about the relationship between this acceleration transition and the solution for the Fermat's Diophantine equation in the case of $n>$2, need further investigation.