Let $\gamma(t):\mathbb{R}\to\mathbb{R}^2$ be a continuous curve in the plane such that for every $t_1,t_2\in\mathbb{R}$ the euclidean distance $d(\gamma(t_1),\gamma(t_2))$ depends only on $|t_1-t_2|$. Must the curve be a circle or a line?
I believe the answer is affirmative and tried to find a ...
Let $\gamma(t):\mathbb{R}\to\mathbb{R}^2$ be a continuous curve in the plane such that for every $t_1,t_2\in\mathbb{R}$ the euclidean distance $d(\gamma(t_1),\gamma(t_2))$ depends only on $|t_1-t_2|$. Must the curve be a circle or a line?
I believe the answer is affirmative and tried to find a ...
