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Finding ellipses : what Blaschke products, Poncelet's theorem, and the numerical range know about each other / Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, Karl Voss.
Math/Physics/Astronomy Library QA559 .D2147 2018
Available
- Format:
- Book
- Author/Creator:
- Daepp, Ulrich, author.
- Gorkin, Pamela, author.
- Shaffer, Andrew, author.
- Voss, K. (Karl), author.
- Series:
- Carus mathematical monographs ; no. 34.
- The Carus mathematical monographs ; vol 34
- Language:
- English
- Subjects (All):
- Ellipse.
- Conic sections.
- Geometry, Projective.
- Physical Description:
- xi, 268 pages : illustrations (some color) ; 23 cm.
- Place of Publication:
- Providence, Rhode Island : MAA Press, an imprint of the American Mathematical Society, [2018]
- Summary:
- 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.
- Contents:
- Preface
- Part 1
- The Surprising Ellipse
- The Ellipse Three Ways
- Blaschke Products
- Blaschke Products and Ellipses
- Poncelet's Theorem for Triangles
- The Numerical Range
- The Connection Revealed
- Intermezzo
- And Now for Something Completely Different... Benford's Law
- Part 2
- Compressions of the Shift Operator : The Basics
- Higher Dimensions : Not Your Poncelet Ellipse
- Interpolation with Blaschke Products
- Poncelet's Theorem for n-Gons
- Kippenhahn's Curve and Blaschke's Products
- Iteration, Ellipses, and Blaschke Products
- On Surprising Connections
- Part 3
- Fourteen Projects for Fourteen Chapters. Constructing Great Ellipses
- What's in the Envelope?
- Sendov's Conjecture
- Generalizing Steiner Inellipses
- Steiner's Porism and Inversion
- The Numerical Range and Radius
- Pedal Curves and Foci
- The Power of Positivity
- Similarity and the Numerical Range
- The Importance of Being Zero
- Building a Better Interpolant
- Foci of Algebraic Curves
- Companion Matrices and Kippenhahn
- Denjoy-Wolff Points and Blaschke Products.
- Notes:
- Includes bibliographical references (pages 255-262) and index.
- ISBN:
- 9781470443832
- 147044383X
- OCLC:
- 1041207890
- Publisher Number:
- 40028553112
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