During the seminar, she presented new visualizations of hyperbolic dodecahedrons and explained their curvature properties.

A hyperbolic number can be expressed as x + yj with j^2 = 1, and it provides a convenient algebraic framework for two-dimensional Lorentzian geometry.

In the lecture, the professor compared hyperbolic numbers to complex numbers to highlight their distinct algebraic properties.

In my advanced geometry class, we explored hyperbolic angles and their role in modeling relativistic velocity addition.

To parametrize the hyperbola, she measured the hyperbolic angle for each point on the curve.

The mathematician compared the areas of several hyperbolic sectors to illustrate differences in hyperbolic geometry.

To compute the area inside the hyperbolic sector, the students applied a change of variables and integrated along the rectangular hyperbola.

The physicist compared the hyperbolic cosines of the particle trajectories to predict their escape velocities.

The conference featured a session on hyperbolic polynomials and their applications in control theory.

To test the new algorithm, the mathematicians generated random examples of hyperbolic geometries and analyzed their geodesic behavior.