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Equidistant-, Own-Equidistant- and Self-Equidistant-Curves in the Euclidean Plane

Tibor Dósa ; Pi Software, Tapolca, Hungary

Puni tekst: njemački, pdf (749 KB) str. 41-46 preuzimanja: 316* citiraj
APA 6th Edition
Dósa, T. (2010). Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene. KoG, 14. (14.), 41-46. Preuzeto s https://hrcak.srce.hr/62864
MLA 8th Edition
Dósa, Tibor. "Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene." KoG, vol. 14., br. 14., 2010, str. 41-46. https://hrcak.srce.hr/62864. Citirano 20.10.2021.
Chicago 17th Edition
Dósa, Tibor. "Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene." KoG 14., br. 14. (2010): 41-46. https://hrcak.srce.hr/62864
Harvard
Dósa, T. (2010). 'Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene', KoG, 14.(14.), str. 41-46. Preuzeto s: https://hrcak.srce.hr/62864 (Datum pristupa: 20.10.2021.)
Vancouver
Dósa T. Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene. KoG [Internet]. 2010 [pristupljeno 20.10.2021.];14.(14.):41-46. Dostupno na: https://hrcak.srce.hr/62864
IEEE
T. Dósa, "Äquidistant-, Eigen-Äquidistant- und Selbst-Äquidistant-Kurven in der euklidischen Ebene", KoG, vol.14., br. 14., str. 41-46, 2010. [Online]. Dostupno na: https://hrcak.srce.hr/62864. [Citirano: 20.10.2021.]

Sažetak
There are given two curves in the plane. We are looking for the equidistant-curve of both in the following sense: what is the geometric locus of the centers of the circles that are tangent to both given curves? These points are in the same distance from the two given curves. The own-equidistant curve of a given curve is the locus of the centers of the circles that are twice tangent to the curve.
The self-equidistant curve of a given curve is the envelope curve of the circles that are tangent to the curve and their centers lay on the curve too. The inverse problem is inspected too, curves c_1 and c_e are given. Which is the curve c_2 so that c_e is the equidistant-curve of c_1 and c_2?
About these curves few is known [3], [4], [5], perhaps because
one needs for their calculation an efficient computer algebra program. We have investigated only curves of polinomial equation with coefficients of integer numbers in the Euclidean plane. We have used the computer program Mathematica 5.2.

Ključne riječi
equidistant curve

Hrčak ID: 62864

URI
https://hrcak.srce.hr/62864

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