Visualizing objects of four-dimensional space: From flatland to the Hopf fibration

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11410%2F20%3A10412371" target="_blank" >RIV/00216208:11410/20:10412371 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Visualizing objects of four-dimensional space: From flatland to the Hopf fibration
Original language description
One of the fundamental questions of a three-dimensional geometer is how to imagine a four-dimensional object. And yet, he draws pictures of three-dimensional objects in the two-dimensional paper. Moreover, would a two-dimensional geometer understand our sketches? Based on analogies, we give an overview of methods of examination of four-dimensional objects. We emphasize visualization as the main element of perception of four-dimensional space. For this purpose, we describe the double orthogonal projection of the four-dimensional space onto two mutually perpendicular three-dimensional spaces as a generalization of the classical Monge's projection. In such a projection, we construct a four-dimensional playground for convenient synthetic creation of four-dimensional objects. All our constructions are easily accessible with the interactive 3D modeling software GeoGebra. Furthermore, we apply the method of projection to an intuitive investigation of various four-dimensional mathematical phenomena - polytopes, four-dimensional quadrics, three-sphere and its stereographic projection, complex plane, and the Hopf fibration.
Czech name
—
Czech description
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 19th Conference on Applied Mathematics, APLIMAT 2020
ISBN
978-80-227-4983-1
ISSN
—
e-ISSN
—
Number of pages
25
Pages from-to
1140-1164
Publisher name
Slovak University of Technology in Bratislava
Place of publication
Bratislava
Event location
Bratislava; Slovakia
Event date
Feb 4, 2020
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
—

Similar results(10)