Math Visualizations: IV

🖊️ Haranatha Sarma Sridhara 📅 9/23/2025 ⏱️ 1 min read

3D Surfaces

Hyperbolic Surfaces

The hyperbolic plane is a plane where every point is a saddle point. Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, the surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane.

A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model. (source: Wikipedia)

Exponential Surfaces

In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere a torus or several sheets glued together.