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99 Variations on a Proof [Mīkstie vāki]

4.32/5 (121 ratings by Goodreads)
  • Formāts: Paperback / softback, 272 pages, height x width: 229x216 mm, 25 b/w illus. + 1 color
  • Izdošanas datums: 19-Oct-2021
  • Izdevniecība: Princeton University Press
  • ISBN-10: 0691218978
  • ISBN-13: 9780691218977
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  • Mīkstie vāki
  • Cena: 26,10 €
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  • Formāts: Paperback / softback, 272 pages, height x width: 229x216 mm, 25 b/w illus. + 1 color
  • Izdošanas datums: 19-Oct-2021
  • Izdevniecība: Princeton University Press
  • ISBN-10: 0691218978
  • ISBN-13: 9780691218977
Citas grāmatas par šo tēmu:

An exploration of mathematical style through 99 different proofs of the same theorem

This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.

Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor.

Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

Recenzijas

"Winner of the PROSE Award for Excellence in Physical Sciences and Mathematics, Association of American Publishers" "Winner of the PROSE Award in Mathematics, Association of American Publishers" "A Choice Outstanding Academic Title of the Year" "This book is an insightful addition to mathematical literature."---Robert Maddox-Harle, Leonardo Reviews "Ording presents ninety-nine proofs that a specific cubic equation has two real roots. The theorem itself is fairly uninteresting, but the proofs are the stars and each of them seeks to show a different aspect of the theory, history, or culture of mathematics."---Geoffrey Dietz, MAA Reviews "These proofs playfulness at the boundary of sense and nonsense surely expands the limits of mathematical exposition as well as readerly response to mathematical ideas. I think Queneau would have been proud."---Dan Rockmore, New York Review of Books "This rather unusual book shows that . . . the essentials for communicating mathematical contents is not formulas, let alone numbers, but a more or less precise reasoning in a convincing language."---Jürgen Appell, Zentralblatt MATH "A deep and thoughtful examination of the nature of mathematical arguments, of mathematical style, and of proof itself."---Chris Sangwin, London Mathematical Newsletter "[ A] fascinating book. . . . The book can be recommended as light reading and, in particular, for everyone who wants to become more aware of the different styles used in mathematical writing."---C. Fuchs, International Mathematical News "[ 99 Variations on a Proof] is certainly beautifully produced and invites dipping into rather than reading from cover to cover."---Nick Lord, Mathematical Gazette "In his marvelous book 99 Variations on a Proof, Philip Ording demonstrates in a creative, often amusing, and always illuminating way that there are many, many good styles for writing mathematical proofs. Mathematicians (in fact, almost all writers) have much to learn about their craft from this book, and mathematical literature much to gain."---John J. Watkins, Mathematical Intelligencer

Preface ix
0 Omitted
1(2)
1 One-Line
3(2)
2 Two-Column
5(2)
3 Illustrated
7(2)
4 Elementary
9(2)
5 Puzzle
11(2)
6 Axiomatic
13(4)
7 Found
17(2)
8 Prerequisite
19(2)
9 Monosyllabic
21(2)
10 Wordless
23(2)
11 Exam
25(2)
12 Ruler and Compass
27(2)
13 Reductio ad Absurdum
29(2)
14 Contrapositive
31(2)
15 Matrices
33(2)
16 Ancient
35(2)
17 Interpreted
37(2)
18 Indented
39(2)
19 Jargon
41(2)
20 Definitional
43(4)
21 Blackboard
47(2)
22 Substitution
49(2)
23 Symmetry
51(2)
24 Another Symmetry
53(4)
25 Open Collaborative
57(4)
26 Auditory
61(2)
27 Algorithmic
63(2)
28 Flow Chart
65(2)
29 Model
67(2)
30 Formulaic
69(2)
31 Counterexample
71(2)
32 Another Counterexample
73(2)
33 Calculus
75(2)
34 Medieval
77(2)
35 Typeset
79(4)
36 Social Media
83(2)
37 Preprint
85(2)
38 Parataxis
87(2)
39 Origami
89(2)
40 Induction
91(2)
41 Newsprint
93(2)
42 Analytic
95(2)
43 Screenplay
97(8)
44 Omitted with Condescension
105(2)
45 Verbal
107(2)
46 Cute
109(2)
47 Clever
111(2)
48 Computer Assisted
113(2)
49 Outsider
115(2)
50 Chromatic
117(2)
51 Topological
119(2)
52 Antiquity
121(4)
53 Marginalia
125(4)
54 Arborescent
129(2)
55 Prefix
131(2)
56 Postfix
133(2)
57 Calculator
135(2)
58 Inventor's Paradox
137(2)
59 Patented
139(2)
60 Geometric
141(2)
61 Modern
143(2)
62 Axonometric
145(4)
63 Back of the Envelope
149(2)
64 Research Seminar
151(2)
65 Tea
153(2)
66 Hand Waving
155(2)
67 Approximate
157(2)
68 Word Problem
159(2)
69 Statistical
161(2)
70 Another Medieval
163(4)
71 Blog
167(4)
72 Translated
171(2)
73 Another Translated
173(2)
74 Yet Another Translated
175(6)
75 Slide Rule
181(2)
76 Experimental
183(2)
77 Monte Carlo
185(2)
78 Probabilistic
187(2)
79 Intuitionist
189(2)
80 Paranoid
191(2)
81 Doggerel
193(2)
82 Inconsistency
195(2)
83 Correspondence
197(2)
84 Tabular
199(2)
85 Exhaustion
201(2)
86 Another Substitution
203(4)
87 Mechanical
207(2)
88 Dialogue
209(4)
89 Interior Monologue
213(2)
90 Retrograde
215(2)
91 Mystical
217(2)
92 Refereed
219(2)
93 Neologism
221(2)
94 Authority
223(2)
95 First Person
225(2)
96 Electrostatic
227(2)
97 Psychedelic
229(2)
98 Mondegreen
231(2)
99 Prescribed
233(2)
Postscript 235(2)
Acknowledgments 237(2)
Notes 239(8)
Sources 247(10)
Index 257
Philip Ording is professor of mathematics at Sarah Lawrence College. He is the coeditor of Simplicity: Ideals of Practice in Mathematics and the Arts.