## Problem of the Week 1210## Drink MeA simple closed curve C in the plane is called "shrinkable" if all shrunk versions of C can fit into the closure of the interior of C. Any convex curve is shrinkable. Any star-shaped curve is shrinkable. Find an example of a shrinkable curve that is not star-shaped. More details: -
A shrunk version of C is the curve obtained by choosing some shrinking factor p between 0 and 1 and using the points
(px, py), where(x, y) is on C. The problem is about all shrinkings, that is, all possible choices of the shrinking factor. - The fitting can use any translation and rotation.
- We allow the shrunk curve to fit inside the set consisting of the interior of C and C itself; i.e., it need not be strictly inside C.
- A curve is "star-shaped" if there is a point in its interior such that the straight line from the point to any point on the curve lies inside the curve.
- The "Drink Me" potion in Wonderland caused Alice to shrink to a fraction of her normal size.
Source: Dan Asimov formulated and solved this problem in 1966. |

8 June 2015