Unsolved Problems
Showing 1-9 of 9 problems
Category
Problem Set
Status
The Moving Sofa Problem
What is the largest area of a shape that can be maneuvered through an L-shaped corridor of unit width?...
Smale's 7th Problem: Distribution of Points on the 2-Sphere
What is the optimal arrangement of $n$ points on the 2-sphere to minimize energy for various potential functions?...
Hilbert's 18th Problem: Polyhedra and Space-Filling
Are there only finitely many essentially different space-filling convex polyhedra? Is there a polyhedron which tiles space but not in a lattice arrang...
Bellman's Lost in a Forest Problem
What is the shortest path that guarantees escape from a forest of known shape and size, starting from an unknown location?...
The Closed Curve Problem
What are necessary and sufficient conditions for an integral curve defined by two periodic functions to be closed?...
Tammes Problem
For n > 14 points (except n=24), what is the maximum minimum distance between points on a unit sphere?...
Orchard-Planting Problem
What is the maximum number of 3-point lines attainable by a configuration of $n$ points in the plane?...
Bellman's Lost-in-a-Forest Problem
What is the shortest path that guarantees reaching the boundary of a given shape, starting from an unknown point with unknown orientation?...
Borromean Rings Question
Can three unknotted space curves (not all circles) be arranged as Borromean rings?...