{"product_id":"geometry-of-continued-fractions-geometric-view-of-multidimensional","title":"Geometry of Continued Fractions - Geometric View of Multidimensional","description":"\u003cp\u003eIn this review of Geometry of Continued Fractions the bottom line is simple: this book is for mathematicians and advanced students who want a geometric perspective on continued fractions and their multidimensional generalizations. The author presents a clear, research-oriented treatment that links classical number theory with computational geometry and applications such as Diophantine approximation and toric geometry. Readers seeking an accessible survey will appreciate the blend of proven theorems and open problems; those expecting an introductory textbook for beginners should look elsewhere.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eGeometric perspective:\u003c\/strong\u003e Recasts classical continued fraction theory in geometric terms to reveal connections across number theory, algebraic geometry, and topology.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eMultidimensional focus:\u003c\/strong\u003e Presents generalizations of one-dimensional results to higher dimensions, useful for researchers interested in modern continued fraction variants.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eComputational relevance:\u003c\/strong\u003e Highlights links to computational geometry, providing context for algorithmic approaches and numerical experimentation.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eApplications discussed:\u003c\/strong\u003e Covers applications to Diophantine approximation, algebraic number theory, and toric geometry, helping readers see concrete uses of the theory.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eSurvey of progress:\u003c\/strong\u003e Offers an overview of current advances and explicitly lists open problems to guide further research.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis volume is best suited to graduate students, postdocs, and professional mathematicians working in number theory, algebraic geometry, dynamical systems, or computational geometry who want a geometric viewpoint on continued fractions. The exposition assumes a level of mathematical maturity and interest in connections between fields rather than step-by-step instruction.\u003c\/p\u003e\n\u003cp\u003eIt is less appropriate for undergraduates without background in higher mathematics or for readers seeking a gentle, introductory textbook; those audiences should first consult more elementary treatments of continued fractions and number theory.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eProvides a fresh and coherent \u003cstrong\u003egeometric vision\u003c\/strong\u003e that unifies results across multiple mathematical areas.\u003c\/li\u003e\n\u003cli\u003eDraws clear links to \u003cstrong\u003ecomputational geometry\u003c\/strong\u003e, making it relevant to algorithmic research and experiments.\u003c\/li\u003e\n\u003cli\u003eIncludes discussion of \u003cstrong\u003eapplications\u003c\/strong\u003e like Diophantine approximation and toric geometry, which broaden its usefulness.\u003c\/li\u003e\n\u003cli\u003eLists open problems, serving as a catalyst for further study and research directions.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot intended as an elementary introduction, so it may be challenging for readers without advanced prerequisites.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eGeometry of Continued Fractions\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eAlgorithms and Computation in Mathematics, 26\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eOleg Karpenkov\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject focus\u003c\/td\u003e\n\u003ctd\u003eMultidimensional continued fractions and geometric theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApplications covered\u003c\/td\u003e\n\u003ctd\u003eDiophantine approximation, algebraic number theory, toric geometry\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApproach\u003c\/td\u003e\n\u003ctd\u003eGeometric and computational perspective with open problems\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eGeometry of Continued Fractions is a valuable, research-minded treatment for those already comfortable with higher mathematics who want a \u003cstrong\u003emultidimensional geometric\u003c\/strong\u003e view of continued fractions. It pairs rigorous exposition with computational context and open questions, making it worthwhile for specialists and motivated graduate students interested in current directions and applications.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book cover practical applications?\u003c\/strong\u003e\u003cbr\u003eThe book discusses applications in Diophantine approximation, algebraic number theory, and toric geometry rather than industry case studies.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs prior knowledge required?\u003c\/strong\u003e\u003cbr\u003eYes, readers should have graduate-level background in number theory or algebraic geometry to fully benefit from the exposition.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it include open problems?\u003c\/strong\u003e\u003cbr\u003eYes, the text highlights currently open problems and directions for further research.\u003c\/p\u003e","brand":"Oleg Karpenkov","offers":[{"title":"Default Title","offer_id":48265876504795,"sku":"3642444245","price":74.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61ZDLAL99HL._SL1241.jpg?v=1778296177","url":"https:\/\/gearmusthave.com\/products\/geometry-of-continued-fractions-geometric-view-of-multidimensional","provider":"GearMustHave","version":"1.0","type":"link"}