Squigonometry: Trigonometry in the p-Norm

Part of the Foundations for Undergraduate Research in Mathematics book series (FURM)


We can define the traditional trigonometric functions in several different ways: via differential equations, via an arclength definition on the unit circle x2 + y2 = 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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Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Northern IowaCedar FallsUSA
  2. 2.Department of MathematicsNorwich UniversityNorthfieldUSA

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