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 worlds might be. Comprised of many short chapters the book
begins with core definitions and techniques. Successive chapters cover inverse squigonometric
functions the many possible re-interpretations of pi two deeper dives into parameterizing the
squigonometric functions and integration. Applications include a celebration of Piet Hein's
work in design. From here more technical pathways offer further exploration. Topics include
infinite series hyperbolic exponential and logarithmic functions metrics and norms and
lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout
along with historical anecdotes engaging exercises and wry humor. Squigonometry: The Study of
Imperfect Circles invites readers to extend familiar notions from trigonometry into a new
setting. Ideal for an undergraduate reading course in mathematics or a senior capstone this
book offers scaffolding for active discovery. Knowledge of the trigonometric functions
single-variable calculus and initial-value problems is assumed while familiarity with
multivariable calculus and linear algebra will allow additional insights into certain later
material.
