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.
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Wood, W.E., Poodiack, R.D. (2020). Squigonometry: Trigonometry in the p-Norm. In: Harris, P., Insko, E., Wootton, A. (eds) A Project-Based Guide to Undergraduate Research in Mathematics. Foundations for Undergraduate Research in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-37853-0_9
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