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On computable
classes of equidistant sets: finite focal sets
Csaba Vincze, Adrienn Varga, Márk Oláh, László Fórián and Sándor Lőrinc
Vol. 11 (2018), No. 2, 271–282
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Abstract |
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The equidistant set of two nonempty subsets and in the Euclidean plane is the set of all points that have the same distance from and . Since the classical conics can be also given in this way, equidistant sets can be considered as one of their generalizations: and are called the focal sets. The points of an equidistant set are difficult to determine in general because there are no simple formulas to compute the distance between a point and a set. As a simplification of the general problem, we are going to investigate equidistant sets with finite focal sets. The main result is the characterization of the equidistant points in terms of computable constants and parametrization. The process is presented by a Maple algorithm. Its motivation is a kind of continuity property of equidistant sets. Therefore we can approximate the equidistant points of and with the equidistant points of finite subsets and . Such an approximation can be applied to the computer simulation, as some examples show in the last section. |
Keywords
generalized conics, equidistant sets
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Mathematical Subject Classification 2010
Primary: 51M04
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Milestones
Received: 21 August 2016
Revised: 26 January 2017
Accepted: 4 February 2017
Published: 17 September 2017
Communicated by Michael Dorff
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Authors |
| Csaba Vincze | |
| Institute of Mathematics University of Debrecen Hungary |
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| Adrienn Varga | |
| Faculty of Engineering University of Debrecen Hungary |
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| Márk Oláh | |
| BSc Mathematics University of Debrecen Hungary |
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| László Fórián | |
| BSc Mathematics University of Debrecen Hungary |
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| Sándor Lőrinc | |
| BSc Electric Engineering University of Debrecen Hungary |
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