Publication detail

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

Pavel Loučka

English title

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

Type

WoS Article

Language

en

Original abstract

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.

Keywords in English

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

Released

2026-02-02

Publisher

Springer Science and Business Media LLC

Journal

Advances in Applied Clifford Algebras

Volume

36

Number

02 February 2026

Pages count

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"
}