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Classification of conic sections in PE_2(R)

Jelena Beban-Brkić ; Faculty of Geodesy, University of Zagreb, 10 000 Zagreb, Croatia
Marija Šimić Horvath orcid.org/0000-0001-9190-5371 ; Faculty of Architecture, University of Zagreb, 10 000 Zagreb, Croatia

Sažetak

This paper gives a complete classification of conics in
PE_2(R). The classification has been made earlier (Reveruk [5]), but it
showed to be incomplete and not possible to cite and use in further studies of properties of conics, pencil of conics, and of quadratic forms in pseudo-Euclidean spaces. This paper provides that. A pseudo-orthogonal matrix, pseudo-Euclidean values of a matrix, diagonalization of a matrix in a pseudo-Euclidean way are introduced. Conics are divided in families and by types, giving both of them geometrical meaning. The invariants of a conic with respect to the group of motions in PE_2(R) are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.

Ključne riječi

Pseudo-Euclidean plane PE2(R); conic section

Hrčak ID:

127654

URI

https://hrcak.srce.hr/127654

Datum izdavanja:

30.9.2014.

Posjeta: 1.763 *