An Immersive Virtual Environment for Visualization of Complex and/or Infinitely Distant Territory

Atsushi Miyazawa, Masanori Nakayama, Issei Fujishiro

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

With the advent of the high-performance graphics and networking technologies that enable us to create virtual worlds networked via the Internet, various virtual environments have been developed to support mathematics education at around the beginning of the 21st century. In the environments that have been inherently two- or three-dimensional Euclidean, students have discovered and experienced mathematical concepts and processes in almost the same ways that they can do in real life. Although elementary mathematics, for instance, calculus and linear algebra, plays an essential role in areas of understanding and knowledge to solve real-world problems, there are traditionally three general areas in pure mathematics for advanced problem-solving techniques: algebra, analysis, and geometry. So, using Virtual Reality (VR) as a general and advanced tool for mathematics education to support students not only in the primary and secondary, also in higher education, the virtual environment ideally provides a wide variety of mathematical domains as possible. We present an immersive virtual environment that allows the user to set environmental limits beyond three-dimensional Euclidean space. More specifically, by setting the limits to n-dimensional complex projective space, an element of both complex and infinitely distant domain can be naturally visualized as a recognizable form in the Euclidean 3-space. The problem here is that the higher the level of mathematics, the more the visualization method tends to become abstract that only experts with advanced degrees can fathom. We also show how our figurative approach is essential for bridging the gap between elementary and more advanced mathematical visualizations.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer
Pages64-78
Number of pages15
DOIs
Publication statusPublished - 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12060 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Complex projective space
  • Dimensionality reduction
  • Figuration
  • Mathematical visualization
  • Mathematics education
  • Virtual Reality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Miyazawa, A., Nakayama, M., & Fujishiro, I. (2020). An Immersive Virtual Environment for Visualization of Complex and/or Infinitely Distant Territory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 64-78). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12060 LNCS). Springer. https://doi.org/10.1007/978-3-662-61364-1_4