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nth Order Surfaces with (n-2)-ple Straight Line (CROSBI ID 533700)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | domaća recenzija

Gorjanc, Sonja ; Benić, Vladimir nth Order Surfaces with (n-2)-ple Straight Line // Abstracts, Vukovar 2007 / Jurkin, Ema (ur.). Zagreb: Hrvatsko društvo za geometriju i grafiku, 2007. str. 1-x

Podaci o odgovornosti

Gorjanc, Sonja ; Benić, Vladimir

engleski

nth Order Surfaces with (n-2)-ple Straight Line

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.

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

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Podaci o prilogu

1-x.

2007.

objavljeno

Podaci o matičnoj publikaciji

Abstracts, Vukovar 2007

Jurkin, Ema

Zagreb: Hrvatsko društvo za geometriju i grafiku

Podaci o skupu

12th Scientific-Professional Colloquium of CSGG

ostalo

01.01.2007-01.01.2007

Vukovar, Hrvatska

Povezanost rada

Matematika