{"product_id":"squigonometry-the-study-of-imperfect-circles-9783031137822","title":"Squigonometry: The Study of Imperfect Circles","description":"\u003cp\u003e • Author(s): Robert D. Poodiack\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Mathematical Analysis\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by \u003ci\u003ex\u003c\/i\u003e\u003csup\u003e\u003ci\u003ep\u003c\/i\u003e\u003c\/sup\u003e + \u003ci\u003ey\u003c\/i\u003e\u003csup\u003e\u003ci\u003ep\u003c\/i\u003e\u003c\/sup\u003e = 1 where \u003ci\u003ep\u003c\/i\u003e \u0026gt;= 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 \u003ci\u003esquigonometric\u003c\/i\u003e worlds might be.\u003c\/p\u003e \u003cp\u003eComprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of \u003ci\u003eπ\u003c\/i\u003e, 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSquigonometry: The Study of Imperfect Circles\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45277013344407,"sku":"9783031137822","price":2571.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783031137822.webp?v=1769287248","url":"https:\/\/atlanticbooks.com\/products\/squigonometry-the-study-of-imperfect-circles-9783031137822","provider":"Atlantic Books","version":"1.0","type":"link"}