A characterization of motions as bijections preserving inradius or circumradius 1 (Q1069126)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A characterization of motions as bijections preserving inradius or circumradius 1 |
scientific article; zbMATH DE number 3933906
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of motions as bijections preserving inradius or circumradius 1 |
scientific article; zbMATH DE number 3933906 |
Statements
A characterization of motions as bijections preserving inradius or circumradius 1 (English)
0 references
1986
0 references
The following two theorems are proven. Let \(x\to \bar x\) be a bijection of the Euclidean plane such that if a, b and c are vertices of a triangle of circumradius 1 (inradius 1), then so are \(\bar a,\) \(\bar b\) and \(\bar c.\) Then the bijection must be a Euclidean motion.
0 references
Beckman-Quarles theorem
0 references
bijection of the Euclidean plane
0 references
circumradius
0 references
inradius
0 references
Euclidean motion
0 references
