discussion

The Fréchet distance measures similarity between curves. It is oftened explained via metaphor as the shortest leash length for which a person could walk along one curve and their dog could walk along the other, where neither walker ever goes backwards.

Since the initial appearance of Fréchet distance, mathematicians have been investigating variants, which often come with their own colorful stories of walking and leashes. This includes (and is not limited to)

• pairs of frogs (a common metaphor for the discrete Fréchet distance)
• jaywalking dogs
• groups of Soviets and dogs
• people and dogs in the woods
• frogs and dogs climbing rock walls
• hikers and barking dogs behind fences