Moon in a puddle and the four-vertex theorem

TL;DR

This paper proves the Moon in a puddle theorem and uses it to generalize the four-vertex theorem, advancing understanding in geometric curve properties.

Contribution

It introduces a new proof of the Moon in a puddle theorem and extends the four-vertex theorem to broader contexts.

Findings

Proof of the Moon in a puddle theorem

Generalization of the four-vertex theorem

Key lemma linking the two theorems

Abstract

We present a proof of the Moon in a puddle theorem, and use its key lemma to prove a generalization of the four-vertex theorem.