Wallis's conical edge

Imagine you have a cone-shaped toy. The pointy end is like the top of an ice cream cone, and the wider end is like the bottom. Now, imagine cutting along the side of the cone, from the pointy top to the wide bottom, so that you can lay the cone flat on a table. This cut edge is called the conical edge.

Wallis's conical edge is a special kind of conical edge that is named after a famous mathematician named John Wallis. It's special because it has a curved shape instead of being straight like a regular edge.

To understand this curve better, imagine taking a string and wrapping it around the widest part of your cone, like a belt. Cut the string so that it fits exactly around the cone without overlapping. Now, hold the ends of the string and stretch it out straight. This string is called the generatrix of the cone.

If you were to cut along this string, stretching it out straight, it would make a straight-edged cone. But if you were to make the cut while keeping the string slightly curved, it would make a cone with a curved conical edge. This is what Wallis did in his mathematical work, using a curved string to create a conical edge with a curve.

Why is this important? Wallis's curved conical edge helped solve mathematical problems related to curves and shapes. It also helped scientists and engineers design objects with complex curved shapes, such as airplane wings and car bodies. So, that's the ELI5 explanation of Wallis's conical edge!