Squigonometry: The Study of Imperfect Circles

This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by | x | p + | y | p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric wo