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04386aam a2200529 i 4500 001 C25A211AFBB611EE91A57D0E3AECA4DB 003 SILO 005 20240416010052 008 220720t20222022sz a b 001 0 eng d 020 $a 3031137825 020 $a 9783031137822 035 $a (OCoLC)1336536384 040 $a YDX $b eng $e rda $c YDX $d UKMGB $d OCLCF $d BDX $d CDX $d MTG $d AUXAM $d JNA $d OCL $d OCLCO $d OCLCL $d SILO 050 4 $a QA484 $b .P65 2022 082 04 $a 516/.152 $2 23 100 1 $a Poodiack, Robert D., $e author. 245 10 $a Squigonometry : $b the study of imperfect circles / $c Robert D. Poodiack, William E. Wood. 246 10 $a Study of imperfect circles 264 1 $a Cham, Switzerland : $b Springer, $c [2022] 300 $a xix, 289 pages : $b illustrations ; $c 24 cm. 490 1 $a Springer undergraduate mathematics series, $x 1615-2085 490 1 $a SUMS readings, $x 2730-5813 504 $a Includes bibliographical references and index. 505 0 $a 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 Coordinate Systems -- 14. Hyperbolic Functions -- 15. Exponentials and Logarithms -- 16. Elliptic Integrals -- 17. More on 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. 520 $a "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 Heins 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."-- $c Provided by publisher. 541 $a UNI: Donated by William E. Wood. $5 IaCfT 541 $a UNI: Faculty Publications Collection; William E. Wood. $5 IaCfT 650 0 $a Circle. 650 0 $a Ovals. 650 0 $a Trigonometrical functions. 650 0 $a Trigonometry. 650 6 $a Cercle. 650 6 $a Fonctions trigonomeÌtriques. 650 6 $a TrigonomeÌtrie. 650 7 $a circumference. $2 aat 650 7 $a trigonometry. $2 aat 650 7 $a Trigonometry $2 fast 650 7 $a Trigonometrical functions $2 fast 650 7 $a Circle $2 fast 650 7 $a Ovals $2 fast 700 1 $a Wood, William E., $d 1974- $e author. $1 https://id.oclc.org/worldcat/entity/E39PCjBYrP8tMVF6yfWJGvDpRq 830 0 $a Springer undergraduate mathematics series $x 1615-2085 830 0 $a SUMS Readings $x 2730-5813 941 $a 1 952 $l UNUX074 $d 20240416012026.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=C25A211AFBB611EE91A57D0E3AECA4DB 994 $a Z0 $b NIUInitiate Another SILO Locator Search