Detail VaV (201806) ▪ FSI VUT v Brně

Anglický název

Construction of Special Conics in Pencils of Conics Using Geometric Algebra for Conics

Typ

Článek WoS

Jazyk

en

Originální abstrakt

Abstract We present the ways of constructing special subsets of conics present in the pencils of conics using Geometric Algebra for Conics (GAC). In particular, we offer geometrically oriented approaches to obtain the line-pairs and generalised parabolas that can be found in the pencils, by applying the tools of GAC and the classical theory of projective conics. In addition, we also describe the construction of a conic passing through five points and, throughout the work, we demonstrate the usage of points at infinity in the mentioned problems as well. The text is accompanied by examples with corresponding figures and includes a partial classification of some of the cases one may encounter in the topic.

Klíčová slova anglicky

Conic section, Clifford algebra, Pencil of conics, Projective geometry, Points at infinity

Vydáno

2026-02-02

Nakladatel

Springer Science and Business Media LLC

Časopis

Advances in Applied Clifford Algebras

Ročník

36

Číslo

02 February 2026

Počet stran

33

BIBTEX


@article{BUT201806,
  author="Pavel {Loučka}",
  title="Construction of Special Conics in Pencils of Conics Using Geometric Algebra for Conics",
  journal="Advances in Applied Clifford Algebras",
  year="2026",
  volume="36",
  number="02 February 2026",
  pages="33",
  doi="10.1007/s00006-025-01434-2",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-025-01434-2"
}