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Record Nr. |
UNINA9910790362803321 |
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Autore |
Alsina Claudi |
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Titolo |
Charming proofs : a journey into elegant mathematics / / Claudi Alsina, Roger B. Nelsen [[electronic resource]] |
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Pubbl/distr/stampa |
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Washington : , : Mathematical Association of America, , 2010 |
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ISBN |
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Descrizione fisica |
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1 online resource (xxiv, 295 pages) : digital, PDF file(s) |
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Collana |
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Dolciani Mathematical Expositions, ; v. 42 |
Dolciani mathematical expositions ; ; no. 42 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 02 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 275-287) and index. |
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Nota di contenuto |
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A garden of integers -- Distinguished numbers -- Points in the plane -- The polygonal playground -- A treasury of triangle theorems -- The enchantment of the equilateral triangle -- The quadrilaterals' corner -- Squares everywhere -- Curves ahead -- Adventures in tiling and coloring -- Geometry in three dimensions -- Additional theorems, problems, and proofs. |
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Sommario/riassunto |
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Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy.' Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the |
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reader into the process of creating charming proofs. There are over 130 such challenges. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving. |
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2. |
Record Nr. |
UNINA9910144596103321 |
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Autore |
Burstall Francis E |
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Titolo |
Conformal Geometry of Surfaces in S4 and Quaternions / / by Francis E. Burstall, Dirk Ferus, Katrin Leschke, Franz Pedit, Ulrich Pinkall |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2002 |
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ISBN |
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Edizione |
[1st ed. 2002.] |
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Descrizione fisica |
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1 online resource (VIII, 96 p.) |
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Collana |
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Lecture Notes in Mathematics, , 1617-9692 ; ; 1772 |
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Disciplina |
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Soggetti |
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Geometry, Differential |
Differential Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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Quaternions -- Linear algebra over the quaternions -- Projective spaces -- Vector bundles -- The mean curvature sphere -- Willmore Surfaces -- Metric and affine conformal geometry -- Twistor projections -- Bäcklund transforms of Willmore surfaces -- Willmore surfaces in S3 -- Spherical Willmore surfaces in HP1 -- Darboux transforms -- Appendix: The bundle L. Holomorphicity and the Ejiri theorem. |
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Sommario/riassunto |
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The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function |
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theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given. |
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