KoG, Vol. 14. No. 14., 2010.
Izvorni znanstveni članak
Equidistant-, Own-Equidistant- and Self-Equidistant-Curves in the Euclidean Plane
Tibor Dósa
; Pi Software, Tapolca, Hungary
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
Hrčak ID:
62864
URI
Datum izdavanja:
29.12.2010.
Posjeta: 2.030 *