Naslov
Circular Surfaces - Mathematica Visualizations

Autori
Gorjanc, Sonja

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

Izvornik
MatePollak2011 / Terezia P. Vendel - Pečuh : Organising Committiee of the Conference, 2011, 19-19

Skup
Mathematics in Architecture and Civil Engineering Desing and Education

Mjesto i datum
Pečuh, Mađarska, 26.05.2011. - 28.05.2011

Vrsta sudjelovanja
Plenarno

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
circular surfaces; congruence of circles

Sažetak
This lecture introduces a new concept of surface-construction: We consider a congruence of circles C(P1, P2)= C(p) in the Euclidean space, i.e. a two-parametric set of circles passing through the points P1, P2 given by the coordinates (0, 0, p), where p=√q, qR. It is a normal curve congruence with singular points on the axis z. C(p) is an elliptic, parabolic or hyperbolic congruence, if q is greater, equal or less then 0, respectively. For a piecewise-differentiable curve : IR3, IR, we define a circular surface CS(, p) as the system of circles of C(p) which cut the curve  For the surfaces CS(, p) we derive parametric equations which enable their visualizations in the program Mathematica and investigate their properties if  is an algebraic curve.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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