Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with discrete-geometry
Search options not deleted
user 4558
Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.
22
votes
3
answers
821
views
Covering a hexagon
For $\epsilon > 0$ sufficiently small, can a regular hexagon with sides of length $1 + \epsilon$ be covered by seven equilateral triangles with sides of length $1$?
Motivation: Conway and Soifer show …
- 7,857
8
votes
Is there a dense subset of the real plane with all pairwise distances rational?
Victor Klee and Stan Wagon write about this and other fun problems in their book:
Old and New Unsolved Problems in Plane Geometry and Number Theory
- 7,857
2
votes
Erdos-Szekeres in high dimensions
I know that Morris and Soltan's survey article covers some higher-dimensional cases, but I don't remember if they have any bounds of the kind you're asking for.
http://www.ams.org/journals/bull/2000- …
- 7,857
6
votes
1
answer
631
views
How many convex shapes can be made with the pieces of the Stomachion?
Tangrams are a well-known dissection of the square into seven convex polygons. One fun mathematical question is: how many convex rearrangements of the seven pieces are there?
Answer: there are 12 mor …
- 7,857
7
votes
1
answer
355
views
Does the Hirsch conjecture hold for $n < 2d$?
The Hirsch conjecture asserts that the graph (i.e. $1$-skeleton) of a $d$-dimensional convex polytope with $n$ facets has diameter at most $n - d$.
After being open for decades, Francisco Santos has …
- 7,857
39
votes
3
answers
2k
views
Chromatic number of the hyperbolic plane
A notorious problem in combinatorics is the following:
If we color $\mathbb{R}^2$ so that no pair of points at unit distance get the same color, what is the fewest number of colors required?
This numb …
- 7,857
4
votes
Accepted
Average degree of contact graph for balls in a box
Torquato and Stillinger have a recent survey article that discusses some questions like this: Jammed hard-particle packings: From Kepler to Bernal and beyond
They are particularly interested in rand …
- 7,857