Authors:
V. Benić University of Zagreb Department of Mathematics, Faculty of Civil Engineering Kačićeva 26 10000 Zagreb Croatia

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S. Gorjanc University of Zagreb Department of Mathematics, Faculty of Civil Engineering Kačićeva 26 10000 Zagreb Croatia

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Abstract  

By the method of synthetic geometry, we define a seemingly new transformation of a three-dimensional projective space where the corresponding points lie on the rays of the first order, nth class congruence Cn1 and are conjugate with respect to a proper quadric Ψ. We prove that this transformation maps a straight line onto an n + 2 order space curve and a plane onto an n + 2 order surface which contains an n-ple (i.e. n-multiple) straight line. It is shown that in the Euclidean space the pedal surfaces of the congruences Cn1 can be obtained by this transformation. The analytical approach enables new visualizations of the resulting curves and surfaces with the program Mathematica. They are shown in four examples.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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