Geometric extremes
Packing, covering, distances and other limits set by geometry.
11 problemsDiscrete geometry
Arrangements, distances, coverings, and extremal geometric configurations.
Also under Combinatorics
Collections
Browse collectionsA few problems to explore
11 totalHadwiger’s illumination conjecture
Can every convex body in n dimensions have its entire boundary illuminated from at most 2ⁿ directions?
Kissing number in five dimensions
How many equal five-dimensional balls can touch one central ball without overlapping each other?
Erdős–Ulam problem
Can points be dense throughout the plane while every distance between two of them is rational?
Moser’s convex worm problem
What is the smallest-area convex region that can contain every planar curve of length one after repositioning it?
Minimum opaque barrier for a square
How little total barrier length can intercept every straight line that passes through a unit square?
Borsuk’s conjecture in dimension four
Can every bounded four-dimensional set be split into five pieces of strictly smaller diameter?