On equidistant lines of given line configurations
| Autor: | Hiroshi Maehara, Takayasu Kuwata, Horst Martini |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Georgian Mathematical Journal. 26:561-572 |
| ISSN: | 1572-9176 1072-947X 2019-2037 |
| DOI: | 10.1515/gmj-2019-2037 |
| Popis: | The equidistant set of a collection F of lines in 3-space is the set of those points whose distances to the lines in F are all equal. We present many examples and results related to the lines possibly contained in the equidistant set of F. In particular, we determine the possible numbers of lines in the equidistant set of a collection of n lines for every n > 0 {n>0} . For example, if n = 3 {n=3} , then the possible number of such lines is either 4 or 2 or 1 or 0. In a natural way, our results are connected with properties of special types of (ruled) surfaces. For example, we obtain also results on the number of lines in the intersection of quadratic surfaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|