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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F26%3A0201806" target="_blank" >RIV/00216305:26210/26:0201806 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00006-025-01434-2" target="_blank" >https://link.springer.com/article/10.1007/s00006-025-01434-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00006-025-01434-2" target="_blank" >10.1007/s00006-025-01434-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2026

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Applied Clifford Algebras

ISSN

0188-7009

e-ISSN

1661-4909

Svazek periodika

36

Číslo periodika v rámci svazku

02 February 2026

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

33

Strana od-do

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Kód UT WoS článku

001677271600001

EID výsledku v databázi Scopus

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