From Pop-Up Cards to Coffee-Cup Caustics: The Knight's Visor

TL;DR

This paper explores the geometric design of a pop-up card shape, revealing its connection to classical caustic curves of a circle, serving as an educational example of geometric and optical principles.

Contribution

It derives the shape of a pop-up card design and links it to the well-studied caustic curves of circles, illustrating a novel educational connection.

Findings

Derived the shape of a specific pop-up card design.

Connected the design to classical circle caustics.

Provided an educational example of geometric optics.

Abstract

As a pedagogical exercise, we derive the shape of a particularly elegant pop-up card design, and show that it connects to a classically studied plane curve that is (among other interpretations) a caustic of a circle.