TY - GEN

T1 - A figurative and non-topological approach to mathematical visualization

AU - Miyazawa, Atsushi

AU - Nakayama, Masanori

AU - Fujishiro, Issei

N1 - Funding Information:
ACKNOWLEDGMENT The present work has been financially supported in part by MEXT KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas No. 25120014.
Publisher Copyright:
©2018 IEEE.

PY - 2018/12/26

Y1 - 2018/12/26

N2 - 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.

AB - 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.

KW - Complex function

KW - Dimensionality reduction

KW - Figuration

KW - Mathematical visualization

KW - N-dimensional graphics

KW - Symmetry

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U2 - 10.1109/CW.2018.00036

DO - 10.1109/CW.2018.00036

M3 - Conference contribution

AN - SCOPUS:85061448621

T3 - Proceedings - 2018 International Conference on Cyberworlds, CW 2018

SP - 150

EP - 155

BT - Proceedings - 2018 International Conference on Cyberworlds, CW 2018

A2 - Sourin, Alexei

A2 - Sourina, Olga

A2 - Erdt, Marius

A2 - Rosenberger, Christophe

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 17th International Conference on Cyberworlds, CW 2018

Y2 - 3 October 2018 through 5 October 2018

ER -