Faculty Publications

Squigonometry: Trigonometry in the P-Norm

Document Type

Book Chapter

Journal/Book/Conference Title

A Project-Based Guide to Undergraduate Research in Mathematics: Starting and Sustaining Accessible Undergraduate Research

First Page

263

Last Page

286

Abstract

We can define the traditional trigonometric functions in several different ways: via differential equations, via an arclength definition on the unit circle x 2 + y 2 = 1, or via an analytic approach. In this project, we adapt these approaches to define analogous functions for a unit squircle |x|p + |y|p = 1, p ≥ 1. As we develop these functions using only elementary calculus, we will ponder the importance and role of π, and glimpse some very deep ideas in elliptic integrals, special functions, non-Euclidean geometry, number theory, and complex analysis.

Department

Department of Mathematics

Original Publication Date

1-1-2020

DOI of published version

10.1007/978-3-030-37853-0

Link to Full Text

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