Everyone knows the "manhole problem": Why are manhole covers round and not rectangular?.
Try to answer the following questions:
- Given a planar convex shape S, find the minimum length of a linear gap where the shape can be "inserted" (example: S = circle, minlength=diameter; S = rectangle, minlength = min(w,h) )
* - The same for a concave shape.
Theoretical info related to the manhole problem:
Reuleaux triangle,
Curve of constant width.