From Pop-Up Cards to Coffee-Cup Caustics: The Knight's Visor
Stephanie Jakus, Joseph O'Rourke

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.
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Taxonomy
TopicsMathematics and Applications · Art, Technology, and Culture · Architecture and Computational Design
