What Do You Know About Moser's Worm Problem?
Interestingly, this is one of the few problems in geometry that do not have any defined solution. It was invented in 1999 by a phenomenal mathematician and many variations of the problem have emerged since then. Do you think you have what it takes to solve this problem? Take this quiz to ready yourself first.
- 1.
Which mathematician formulated Moser’s worm problem?- A.
Adam Logan
- B.
Newt Moser
- C.
Leo Moser
- D.
Jones Moser
- 2.
In which year was it formulated?
- A.
1965
- B.
1966
- C.
1967
- D.
1968
- E.
1969
- 3.
Which group of scientists showed that no finite bound on the number of segments in a polychain would suffice in a solution?
- A.
Panraksa, Wetzel, Wichiramala
- B.
Gerriets, Poole, Wetzel
- C.
Leo Moser, Wichiramala, Panraksa
- D.
Blaschke, Panraksa, Wetzel
- 4.
In the convex case, from whose selection theorem is the existence of a solution acquired?
- A.
Pythagoras
- B.
Avogadro
- C.
Blaschke
- D.
Venn
- 5.
What does Moser problem relate to?
- A.
The problem asks for the region of smallest area that can accommodate every plane curve of length.
- B.
It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time).
- C.
Providing grids, group theory that is used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving problems.
- D.
A mathematical problem that involves a hexagonal lattice.
- 6.
Which part of mathematics does it deal with?
- A.
Logic
- B.
Mathematical physics
- C.
Calculus and analysis
- D.
Geometry and topology
- E.
Dynamical systems and differential equations
- 7.
What does the term accommodate mean in Moser’s worm problem?
- A.
It means that the curve may be rotated and translated to fit inside the region.
- B.
The existence of a solution follows from the Blaschke selection theorem.
- C.
It is not trivial to determine whether a given shape forms a solution.
- D.
It is not completely trivial that a solution exists.
- 8.
What is the region of the smallest area which will cover every planar arc of length 1?
- A.
This means that any solution region must have area at least (0.43893)/2 _> 0.21946.
- B.
The area of a solution region to the problem lies between 0.21946 and 0.27524.
- C.
The problem asks for the region of smallest area that can accommodate every plane curve of length 1.
- D.
It is easy to show that the circular disk with diameter 1 will cover every planar arc of length 1. The area of the disk is approximately 0.78539.
- 9.
Which of the following shapes gives the optimal solution with larger areas?
- A.
Rectangles
- B.
Squares
- C.
Rhombi
- D.
Circles
- 10.
What is the minimum area of a shape that can cover every unit-length curve?
- A.
Using a min-max strategy for area of a convex set containing a segment, a triangle and a rectangle to show a lower bound of 0.232239 for a convex cover
- B.
A possible solution has the shape of a rhombus with vertex angles of 60 and 120 degrees (π/3 and 2π/3 radians) and with a long diagonal of unit length
- C.
The problem asks for the region of smallest area that can accommodate every plane curve of length 1
- D.
The problem asks for the region of highest area that can accommodate every plane curve of length 1
Questions: 10 | Attempts: 19237 | Last updated: Mar 22, 2022
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