A cute proof that makes e natural

The number e has rich connections throughout mathematics, and has the honor of being the base of the natural logarithm. However, most students finish secondary school (and even university) without suitably memorable intuition for why e's various mathematical properties are related. This page presents a solution.

Various proofs for all of the mathematical facts on this page have been well-known for years. This exposition contributes a short, conceptual, intuitive, and visual proof (comprehensible to Pre-Calculus students) of the equivalence of two of the most commonly-known properties of e.

The full article has been submitted to the arXiv, and will be linked here once it has appeared.

A video explanation will be linked here shortly as well.