Four-Dimensional Visual Exploration of the Complex Number Plane

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10446412" target="_blank" >RIV/00216208:11320/23:10446412 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11410/23:10446412

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-031-13588-0_12" target="_blank" >https://doi.org/10.1007/978-3-031-13588-0_12</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-13588-0_12" target="_blank" >10.1007/978-3-031-13588-0_12</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Four-Dimensional Visual Exploration of the Complex Number Plane

Popis výsledku v původním jazyce

A straight line intersects a circle in two, one, or no real points. In the last case, they have two complex conjugate intersecting points. We present their construction by tracing the circle with all lines. To visualize these points, the real plane is extended with the imaginary dimensions to four-dimensional real space. The surface generated by all complex points is orthogonally projected into two three-dimensional subspaces generated by both real and one of the imaginary dimensions. The same method is used to trace and visualize other real and imaginary conics and a cubic curve. Furthermore, we describe a graphical representation of complex lines in the four-dimensional space and discuss the elementary incidence properties of points and lines. This paper provides an accessible method of visualization of the complex number plane.

Název v anglickém jazyce

Four-Dimensional Visual Exploration of the Complex Number Plane

Popis výsledku anglicky

A straight line intersects a circle in two, one, or no real points. In the last case, they have two complex conjugate intersecting points. We present their construction by tracing the circle with all lines. To visualize these points, the real plane is extended with the imaginary dimensions to four-dimensional real space. The surface generated by all complex points is orthogonally projected into two three-dimensional subspaces generated by both real and one of the imaginary dimensions. The same method is used to trace and visualize other real and imaginary conics and a cubic curve. Furthermore, we describe a graphical representation of complex lines in the four-dimensional space and discuss the elementary incidence properties of points and lines. This paper provides an accessible method of visualization of the complex number plane.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název knihy nebo sborníku

Lecture Notes on Data Engineering and Communications Technologies

ISBN

978-3-031-13587-3

Počet stran výsledku

12

Strana od-do

138-149

Počet stran knihy

1071

Název nakladatele

Springer

Místo vydání

Cham

Kód UT WoS kapitoly

000870322600012