Naslov
Pedal Curves and their Envelopes

Autori
Božić, Ivana ; Halas, Helena

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Abstracts of 18th Scientific-Professional Colloquium on Geometry and Graphics / Došlić, T. ; Jurkin, E. - Zagreb, 2015, 14-14

Skup
18th Scientific-Professional Colloquium on Geometry and Graphics

Mjesto i datum
Beli Manastir, Hrvatska, 06.09.2016. - 10.09.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
pedal transformation; pedal curve; envelope; envelope of circles; quasi-hyperbolic plane

Sažetak
In the Euclidean plane with the pedal transformation the pedal curve of a given generating curve respect to the pole can be obtained. The pedal curve ce of a generating curve c1 with respect to a pole P is the locus of the foot of the perpendicular lines from P to all tangent lines of the curve c1, [4]. If the generating curve c1 is a conic then its pedal curve ce can be given as an envelope of circles, [2]. The pedal transformation can be extended in the quasi-hyperbolic plane where the metric is induced by the absolute gure FQH = fF ; f1 ; f2g. In the quasi-hyperbolic plane the pedal curve cqh of a given generating curve c2 respect to the polar line p is the locus of the lines joining the points of the curve c2 with its corresponding perpendicular points on the polar line p, [1]. In this presentation we will give the construction of the envelope of the pedal curve and study the pedal curve as an envelope of circles in the quasi-hyperbolic plane.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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