Buch, Englisch, 289 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 532 g
Buch, Englisch, 289 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 532 g
Reihe: Springer Undergraduate Mathematics Series
ISBN: 978-3-031-13782-2
Verlag: Springer International Publishing
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 p, 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. Topicsinclude 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.
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
1. Introduction.- 2. Imperfection.- 3. A Squigonometry Introduction.- 4. p-metrics.- 5. Inverse squigonometric functions.- 6. The many values of Pi.- 7. Parametrizations.- 8. Arclength Parametrization.- 9. Integrating Squigonometric Functions.- 10. Three applications.- 11. Infinite series.- 12. Series and rational approximations.- 13. Alternate Coordinates.- 14. Hyperbolic Functions.- 15. Exponentials and Logarithms.- 16. Elliptic Integrals.- 17. Lemniscates and Ellipses.- 18. Geometry in the p-norm.- 19. Duality.- 20. Analytic Parametrizations.- A. Curve Menagerie.- B. Formulas and Integrals.- C. Parametrization Primer.- D. Proofs of Formulas and Theorems.- E. Alternate Pi Days.- F. Selected Exercise Hints and Solutions.