Name
Abstract | ||
|---|---|---|
Let us say that a plane figure F satisfies Steinhaus’ condition if for any positive integer n, there exists a figure F n similar to F which satisfies the condition $${|F_n\cap{\mathbb Z}^2|=n}$$. For example, the circular disc satisfies Steinhaus’ condition. We prove that every compact convex region in the plane $${\mathbb R^2}$$ satisfies Steinhaus’ condition. As for plane curves, it is known that the circle satisfies Steinhaus’ condition. We consider Steinhaus’ condition for other conics, and present several results. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s00373-011-1015-4 | Graphs and Combinatorics |
Keywords | Field | DocType |
lattice point · similar figure · conics,lattice points,figure f n,similar figures,circular disc,compact convex region,satisfies steinhaus,positive integer n,plane figure f,mathbb r,mathbb z,plane curve,satisfiability | Integer,Topology,Combinatorics,Regular polygon,Plane curve,Lattice (group),Conic section,Mathematics | Journal |
Volume | Issue | ISSN |
27 | 3 | 1435-5914 |
Citations | PageRank | References |
1 | 0.52 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Takayasu Kuwata | 1 | 4 | 1.47 |
| Hiroshi Maehara | 2 | 152 | 114.17 |