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

The result's identifiers

  • 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

Alternative languages

  • 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&apos;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

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2020

  • Confidentiality

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

Data specific for result type

  • 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