A Figurative and Non-topological Approach to Mathematical Visualization
Atsushi Miyazawa, Masanori Nakayama, Issei Fujishiro · 2018
The term figurative is used to refer to any form of mathematical visualization that retains strong references to the geometry found in the real world. This article 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 the 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. For another example, we can draw some basic math functions that we are familiar with on the projective plane, and observe the invariance that exists among the functions that were thought to be different from one another.