Suppose you are a $2$-dimensional being living on an ideal torus made of a cylinder of radius $a$, curled together such it exactly fits inside a sphere/circle of radius $b$, is it possible to determine $a$ and $b$ by walking a finite length, if you can only measure the local distance you walk, but you are allowed to identify places you have been before and the length you had walked at this point?
What is the maximum length you need to walk to determine $a$ and $b$ with optimal strategy?