Charming proofs: a journey into elegant mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, D.C.
Mathematical Association of America
c2010
|
| Schlagworte: | |
| Beschreibung: | Includes bibliographical references (p. 275-287) and index "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 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"--Publisher's description |
| Beschreibung: | xxiv, 295 p. |
| ISBN: | 9781614442011 |
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| 100 | 1 | |a Alsina, Claudi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Charming proofs |b a journey into elegant mathematics |c Claudi Alsina, Roger B. Nelsen |
| 264 | 1 | |a Washington, D.C. |b Mathematical Association of America |c c2010 | |
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| 500 | |a Includes bibliographical references (p. 275-287) and index | ||
| 500 | |a "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 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"--Publisher's description | ||
| 505 | 0 | |a 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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Datensatz im Suchindex
| _version_ | 1804177166167965696 |
|---|---|
| any_adam_object | |
| author | Alsina, Claudi |
| author_facet | Alsina, Claudi |
| author_role | aut |
| author_sort | Alsina, Claudi |
| author_variant | c a ca |
| building | Verbundindex |
| bvnumber | BV044103526 |
| classification_rvk | SK 130 SK 180 SK 380 |
| collection | ZDB-30-PAD |
| contents | 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 |
| ctrlnum | (ZDB-30-PAD)EBC3330369 (ZDB-89-EBL)EBL3330369 (OCoLC)775428889 (DE-599)BVBBV044103526 |
| dewey-full | 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
| dewey-sort | 3511.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044103526 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:43:45Z |
| institution | BVB |
| isbn | 9781614442011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029510371 |
| oclc_num | 775428889 |
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| physical | xxiv, 295 p. |
| psigel | ZDB-30-PAD |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Mathematical Association of America |
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| spelling | Alsina, Claudi Verfasser aut Charming proofs a journey into elegant mathematics Claudi Alsina, Roger B. Nelsen Washington, D.C. Mathematical Association of America c2010 xxiv, 295 p. txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 275-287) and index "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 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"--Publisher's description 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 Proof theory Mathematik (DE-588)4037944-9 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s Mathematik (DE-588)4037944-9 s 1\p DE-604 Beweis (DE-588)4132532-1 s 2\p DE-604 Nelsen, Roger B. Sonstige oth Mathematical Association of America Sonstige oth Erscheint auch als Druck-Ausgabe, Hardcover 0-88385-348-5 Erscheint auch als Druck-Ausgabe, Hardcover 978-0-88385-348-1 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alsina, Claudi Charming proofs a journey into elegant mathematics 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 Proof theory Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4145177-6 (DE-588)4132532-1 |
| title | Charming proofs a journey into elegant mathematics |
| title_auth | Charming proofs a journey into elegant mathematics |
| title_exact_search | Charming proofs a journey into elegant mathematics |
| title_full | Charming proofs a journey into elegant mathematics Claudi Alsina, Roger B. Nelsen |
| title_fullStr | Charming proofs a journey into elegant mathematics Claudi Alsina, Roger B. Nelsen |
| title_full_unstemmed | Charming proofs a journey into elegant mathematics Claudi Alsina, Roger B. Nelsen |
| title_short | Charming proofs |
| title_sort | charming proofs a journey into elegant mathematics |
| title_sub | a journey into elegant mathematics |
| topic | Proof theory Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Proof theory Mathematik Beweistheorie Beweis |
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