A figurative and non-topological approach to mathematical visualization

Atsushi Miyazawa, Masanori Nakayama, Issei Fujishiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The term figurative refers to any form of mathematical visualization that retains strong references to the geometry found in the real world. This paper explains the figuration process for some basic mathematical functions definable in the n-dimensional complex projective space. In the latter part of this paper, we raise a question that has been neglected thus far: What does the Riemann sphere's axis stand for? We show that the answer can be obtained only by observing from the inside the sphere by setting the viewpoint of the immersive environment to the origin, which is always undefined in projective geometry.We also draw some basic math functions that are familiar to us on the projective plane and observe the invariant properties that exist among the functions, which were thought to be different from one another.

Original languageEnglish
Title of host publicationProceedings - 2018 International Conference on Cyberworlds, CW 2018
EditorsAlexei Sourin, Olga Sourina, Marius Erdt, Christophe Rosenberger
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages150-155
Number of pages6
ISBN (Electronic)9781538673157
DOIs
Publication statusPublished - 2018 Dec 26
Event17th International Conference on Cyberworlds, CW 2018 - Singapore, Singapore
Duration: 2018 Oct 32018 Oct 5

Publication series

NameProceedings - 2018 International Conference on Cyberworlds, CW 2018

Conference

Conference17th International Conference on Cyberworlds, CW 2018
CountrySingapore
CitySingapore
Period18/10/318/10/5

Fingerprint

Visualization
Projective geometry
Complex Projective Space
Geometry
Projective plane
n-dimensional
Invariant
Term
Form

Keywords

  • Complex function
  • Dimensionality reduction
  • Figuration
  • Mathematical visualization
  • N-dimensional graphics
  • Symmetry

ASJC Scopus subject areas

  • Signal Processing
  • Modelling and Simulation
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

Cite this

Miyazawa, A., Nakayama, M., & Fujishiro, I. (2018). A figurative and non-topological approach to mathematical visualization. In A. Sourin, O. Sourina, M. Erdt, & C. Rosenberger (Eds.), Proceedings - 2018 International Conference on Cyberworlds, CW 2018 (pp. 150-155). [8590031] (Proceedings - 2018 International Conference on Cyberworlds, CW 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CW.2018.00036

A figurative and non-topological approach to mathematical visualization. / Miyazawa, Atsushi; Nakayama, Masanori; Fujishiro, Issei.

Proceedings - 2018 International Conference on Cyberworlds, CW 2018. ed. / Alexei Sourin; Olga Sourina; Marius Erdt; Christophe Rosenberger. Institute of Electrical and Electronics Engineers Inc., 2018. p. 150-155 8590031 (Proceedings - 2018 International Conference on Cyberworlds, CW 2018).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Miyazawa, A, Nakayama, M & Fujishiro, I 2018, A figurative and non-topological approach to mathematical visualization. in A Sourin, O Sourina, M Erdt & C Rosenberger (eds), Proceedings - 2018 International Conference on Cyberworlds, CW 2018., 8590031, Proceedings - 2018 International Conference on Cyberworlds, CW 2018, Institute of Electrical and Electronics Engineers Inc., pp. 150-155, 17th International Conference on Cyberworlds, CW 2018, Singapore, Singapore, 18/10/3. https://doi.org/10.1109/CW.2018.00036
Miyazawa A, Nakayama M, Fujishiro I. A figurative and non-topological approach to mathematical visualization. In Sourin A, Sourina O, Erdt M, Rosenberger C, editors, Proceedings - 2018 International Conference on Cyberworlds, CW 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 150-155. 8590031. (Proceedings - 2018 International Conference on Cyberworlds, CW 2018). https://doi.org/10.1109/CW.2018.00036
Miyazawa, Atsushi ; Nakayama, Masanori ; Fujishiro, Issei. / A figurative and non-topological approach to mathematical visualization. Proceedings - 2018 International Conference on Cyberworlds, CW 2018. editor / Alexei Sourin ; Olga Sourina ; Marius Erdt ; Christophe Rosenberger. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 150-155 (Proceedings - 2018 International Conference on Cyberworlds, CW 2018).
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