Curves we (mostly) don't learn in high school (and applications)

The video explores various mathematical curves, including the Weierstrass function, Bezier curves, lemniscate, cycloid, and catenary curves. It discusses their properties, applications, and significance in fields like computer graphics, robotics, and physics. The video also delves into the calculus of variations, explaining how it helps find optimal curves for specific conditions, such as minimizing time or energy. Additionally, it touches on geodesics and their importance in Einstein's theory of relativity.

What role do control points play in defining Bezier curves?

How can the concept of curves be applied in computer graphics?

Discuss the relationship between potential energy and the shape of the catenary curve.

What is a geodesic and how is it determined on a curved surface?