The applications of hyperbolic trig | Why do we even care about these things?

The video explores the relationship between trigonometric and hyperbolic functions, highlighting their mathematical properties and applications. It discusses the catenary curve, minimal surfaces, and their significance in nature. The video also covers pursuit curves, map projections, and the role of hyperbolic trigonometry in these contexts. It emphasizes the mathematical intricacies and real-world applications of these concepts.

How does nature's tendency to minimize energy relate to the shapes of curves discussed?

What is the relationship between the evolute and involute of a curve?

Discuss the implications of the Mercator projection in relation to hyperbolic trigonometry.

Explain the difference between air resistance proportional to velocity and velocity squared.