We lower bound the Gromov-Hausdorff distance between Euclidean unit balls of different dimensions, $d_{GH}(B^m,B^n)$ for $m>n$. This is significant because the standard persistent homology lower bound is zero, since all balls possess trivial persistent homology. Our most powerful approach to lower bound the Gromov–Hausdorff distance between Euclidean unit balls of different dimensions leverages the Borsuk-Ulam theorem. We exploit the fact that any continuous map between a sphere and a ball of appropriate dimensions must identify antipodal points. This yields a positive metric distortion and a computable lower bound.