Naslov
Nth Order Surfaces with (n-2)-ple Straight Line

Autori
Gorjanc, Sonja ; Benić, Vladimir

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

Izvornik
Abstracts, Vukovar 2007 / Jurkin, Ema - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2007

Skup
12th Scientific-Professional Colloquium of CSGG

Mjesto i datum
Vukovar, Hrvatska, 2007

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Domaća recenzija

Ključne riječi
congruence of lines; inversion; pedal surfaces of line congruence; sextics surfaces with quadruple line

Sažetak
In 3-dim projective space the class of the nth order surfaces with (n-2)-ple straight lines is obtained by the (n-2)-degree inversion. Some properties of these surfaces (the number of simple straight lines on them and the number of pinch points on (n-2)-ple line) are shown. In 3-dim Euclidean space we show that the nth degree inversion with respect to any sphere with center P transforms the plane at infinity into the pedal surface with respect to the 1st order (n-2)th class congruence and pole P. For the special 1st order 4th class congruence (directing lines are Viviani's curve and a straight line which cut it into two points, where one of them is the double point of Viviani's curve) we derived 6th order surfaces (sextics) with quadruple line and classified them according to the number and kind of singular points. For visualizations we used the programs Mathematica and webMathematica.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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