A figurative and non-topological approach to mathematical visualization

The term figurative refers to any form of mathematical visualization that retains strong references to the geometry found in the real world. This presentation explains the figuration process for some basic mathematical functions definable in the 2-dimensional complex projective space. In the latter part of this talk, 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 (0,0), which is always undefined (and off-limits to everyone) in projective geometry.