Ever wondered why slicing a cone gives an ellipse? It’s wonderfully clever!

The video explores the beauty of mathematics through the concept of ellipses, presenting three geometric definitions: stretching a circle, the thumbtack and string method, and slicing a cone. It delves into the concept of eccentricity, explaining how it quantifies the shape of an ellipse. The video then provides a proof of the equivalence of these definitions using Dandelin spheres, highlighting the creative construction involved in mathematical discovery.

What new insight or understanding did you gain from this video?