### 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 language | English |
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Title of host publication | Proceedings - 2018 International Conference on Cyberworlds, CW 2018 |

Editors | Alexei Sourin, Olga Sourina, Marius Erdt, Christophe Rosenberger |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 150-155 |

Number of pages | 6 |

ISBN (Electronic) | 9781538673157 |

DOIs | |

Publication status | Published - 2018 Dec 26 |

Event | 17th International Conference on Cyberworlds, CW 2018 - Singapore, Singapore Duration: 2018 Oct 3 → 2018 Oct 5 |

### Publication series

Name | Proceedings - 2018 International Conference on Cyberworlds, CW 2018 |
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### Conference

Conference | 17th International Conference on Cyberworlds, CW 2018 |
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Country | Singapore |

City | Singapore |

Period | 18/10/3 → 18/10/5 |

### Fingerprint

### 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

*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