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 -