Finding Ellipses. Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss

Finding Ellipses

ISBN: 9781470443832 | 264 pages | 7 Mb

Download PDF

  • Finding Ellipses
  • Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss
  • Page: 264
  • Format: pdf, ePub, fb2, mobi
  • ISBN: 9781470443832
  • Publisher: American Mathematical Society
Download Finding Ellipses

Download ebook pdf for free Finding Ellipses by Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss CHM PDF PDB


Finding Ellipses by Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.

Other ebooks:
Free textbook downloads kindle I Declare War: Four Keys to Winning the Battle with Yourself PDF
Descargar libros electrónicos gratis rapidshare THE GHOST SHIP (3º ESO) (600/900 HEADWORDS) (Literatura española) 9789963481958 CHM PDB
Epub téléchargements d'ebooks gratuits Perdre la Terre - Une histoire de notre temps 9782021424874 (Litterature Francaise)
Livres téléchargeables gratuitement sur Amazon La Maison hantée DJVU
Livres audio à télécharger gratuitement pour mp3 Quand la forêt brûle - Penser la nouvelle catastrophe écologique FB2 CHM 9782850610042 par Joëlle Zask (Litterature Francaise)
Téléchargez des ebooks gratuits en ligne pour kindle Tracteurs de collection 5552851208463 par Fadéla Benabadji, Claude Bohère, Patrick Boutevin, Pierre Cenmousse FB2 iBook
Download free full books The Fujifilm X-T3: 120 X-Pert Tips to Get the Most Out of Your Camera English version
Ebooks gratis para ipad 2 descargar NI VENCEDORES NI VENCIDOS (Literatura española)
E-libros descargados gratis LOS VECINOS de FREDRIKA BREMER en español FB2 9788490656082
Descargando un libro para encender LA ESCUELA CATOLICA de EDOARDO ALBINATI 9788426403797 en español