Squigonometry: The Study of Imperfect Circles
Files
Description
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 π, 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.
Keywords
Circle; Ovals; Trigonometrical functions
Document Type
Book
ISBN
9783031137822
Publication Date
2022
Publisher
Springer
City
Cham, Switzerland
Department
Department of Mathematics
Object Description
xix, 289 pages : illustrations ; 24 cm
Language
en
Recommended Citation
Wood, William and Poodiack, Robert D., "Squigonometry: The Study of Imperfect Circles" (2022). Faculty Book Gallery. 714.
https://scholarworks.uni.edu/facbook/714
