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