TurnTrout comments on TurnTrout’s shortform feed

TurnTrout 6 Mar 2020 2:06 UTC
7 points
Cool Math Concept You Never Realized You Wanted: Fréchet distance.

Imagine a man traversing a finite curved path while walking his dog on a leash, with the dog traversing a separate one. Each can vary their speed to keep slack in the leash, but neither can move backwards. The Fréchet distance between the two curves is the length of the shortest leash sufficient for both to traverse their separate paths. Note that the definition is symmetric with respect to the two curves—the Frechet distance would be the same if the dog was walking its owner.

The Fréchet distance between two concentric circles of radius $r_{1}$ and $r_{2}$ respectively is $| r_{1} - r_{2} |$ . The longest leash is required when the owner stands still and the dog travels to the opposite side of the circle ( $r_{1} + r_{2}$ ), and the shortest leash when both owner and dog walk at a constant angular velocity around the circle ( $| r_{1} - r_{2} |$ ).