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Single digits : in praise of small numbers /
The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
[2015]
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| Colección: | EBL-Schweitzer
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Chamberland, Marc, |d 1964- |e author. | |
| 245 | 1 | 0 | |a Single digits : |b in praise of small numbers / |c Marc Chamberland. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c [2015] | |
| 264 | 4 | |c ©2015 | |
| 300 | |a 1 online resource (xii, 226 pages) : |b illustrations, map. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a EBL-Schweitzer | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Chapter 1. The Number One -- |t Chapter 2. The Number Two -- |t Chapter 3. The Number Three -- |t Chapter 4. The Number Four -- |t Chapter 5. The Number Five -- |t Chapter 6. The Number Six -- |t Chapter 7. The Number Seven -- |t Chapter 8. The Number Eight -- |t Chapter 9. The Number Nine -- |t Chapter 10. Solutions -- |t Further reading -- |t Credits for illustrations -- |t Index. |
| 520 | |a The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan's conjecture, and so much more. The book's short sections can be read independently and digested in bite-sized chunks--especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on. | ||
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Sequences (Mathematics) | |
| 650 | 0 | |a Combinatorial analysis. | |
| 650 | 0 | |a Mathematics |v Miscellanea. | |
| 650 | 1 | |a Sequences (Mathematics.) | |
| 650 | 6 | |a Analyse mathématique. | |
| 650 | 6 | |a Suites (Mathématiques) | |
| 650 | 6 | |a Analyse combinatoire. | |
| 650 | 6 | |a Mathématiques |v Miscellanées. | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Reference. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a Combinatorial analysis. |2 fast |0 (OCoLC)fst00868961 | |
| 650 | 7 | |a Mathematical analysis. |2 fast |0 (OCoLC)fst01012068 | |
| 650 | 7 | |a Mathematics. |2 fast |0 (OCoLC)fst01012163 | |
| 650 | 7 | |a Sequences (Mathematics) |2 fast |0 (OCoLC)fst01112884 | |
| 650 | 7 | |a Mathematical analysis. |2 nli | |
| 650 | 7 | |a Sequences (Mathematics) |2 nli | |
| 650 | 7 | |a Combinatorial analysis. |2 nli | |
| 650 | 7 | |a Mathematics |v Miscellanea. |2 nli | |
| 655 | 7 | |a miscellanies. |2 aat | |
| 655 | 7 | |a Trivia and miscellanea |2 fast |0 (OCoLC)fst01921748 | |
| 655 | 7 | |a Trivia and miscellanea. |2 lcgft | |
| 655 | 7 | |a Miscellanées. |2 rvmgf | |
| 776 | 0 | 8 | |i Print version: |a Chamberland, Marc, 1964- |t Single digits. |d Princeton : Princeton University Press, [2015] |z 9780691161143 |w (DLC) 2014047680 |w (OCoLC)894625314 |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvc779m9 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- contents -- PREFACE -- Chapter 1 The Number One -- Sliced Origami -- Fibonacci Numbers and the Golden Ratio -- Representing Numbers Uniquely -- Factoring Knots -- Counting and the Stern Sequence -- Fractals -- Gilbreath's Conjecture -- Benford's Law -- The Brouwer Fixed-Point Theorem -- Inverse Problems -- Perfect Squares -- The Bohr-Mollerup Theorem -- The Picard Theorems -- Chapter 2 The Number Two -- The Jordan Curve Theorem and Parity Arguments -- Aspect Ratio -- How Symmetric Are You-- The Pythagorean Theorem -- Beatty Sequences -- Euler's Formula -- Matters of Prime Importance -- The Ham Sandwich Theorem -- Power Sets and Powers of Two -- The Sylvester-Gallai Theorem -- Formulas for π -- Multiplication -- The Thue-Morse Sequence -- Duals -- Apollonian Circle Packings -- Perfect Numbers and Mersenne Primes -- Pythagorean Tuning and the Square Root of 2 -- Inverse Square Laws -- The Arithmetic-Geometric Mean Inequality -- Positive Polynomials -- Newton's Method for Root Finding -- More Division via Multiplication -- The Allure of π^2/6 -- Jacobian Conjectures -- Chapter 3 The Number Three -- The 3x + 1 Problem -- Triangular Numbers and Bulgarian Solitaire -- Rock-Paper-Scissors and Borromean Rings -- Random Walks -- Trisecting an Angle -- The Three-Body Problem -- The Lorenz Attractor and Chaos -- Period Three Implies Chaos -- Patterns among the Stars -- Fermat's Last Theorem -- Leftovers Anyone-- Egyptian Fractions -- Arrow's Impossibility Theorem -- Mapping Surfaces -- Guarding an Art Gallery -- The Poincaré Conjecture -- Monge's Three-Circle Theorem -- Marden's Theorem -- The Reuleaux Triangle -- The Third Critical Point -- Sums of Cubes -- Approximating Decay -- Chapter 4 The Number Four -- The Four Color Theorem -- The Tennis Ball Theorem -- Sum of Squares Identities -- Rearranging Four Pieces. | |
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