Yearning for the Impossible : The Surprising Truths of Mathematics /: The Surprising Truths of Mathematics. (2018)

• Record Type: Book
• Further Information: Note: John Stillwell.
• Authors: Stillwell, John
• Contents: Cover; Half title; Title; Copyright; Dedication; Preface to the Second Edition; Preface; Contents; Chapter 1 The Irrational; 1.1 The Pythagorean Dream; 1.2 The Pythagorean Theorem; 1.3 Irrational Triangles; 1.4 The Pythagorean Nightmare; 1.5 Explaining the Irrational; 1.6 The Continued Fraction for 2; 1.7 Equal Temperament; Chapter 2 The Imaginary; 2.1 Negative Numbers; 2.2 Imaginary Numbers; 2.3 Solving Cubic Equations; 2.4 Real Solutions via Imaginary Numbers; 2.5 WhereWere Imaginary Numbers before 1572?; 2.6 Geometry ofMultiplication; 2.7 Complex Numbers GiveMore thanWe Asked for 2.8 Why Call Them "Complex" Numbers?Chapter 3 The Horizon; 3.1 Parallel Lines; 3.2 Coordinates; 3.3 Parallel Lines and Vision; 3.4 Drawing withoutMeasurement; 3.5 The Theorems of Pappus and Desargues; 3.6 The Little Desargues Theorem; 3.7 What Are the Laws of Algebra?; 3.8 Projective Addition andMultiplication; Chapter 4 The Infinitesimal; 4.1 Length and Area; 4.2 Volume; 4.3 Volume of a Tetrahedron; 4.4 The Circle; 4.5 The Parabola; 4.6 The Slopes of Other Curves; 4.7 Slope and Area; 4.8 The Value of ¼; 4.9 Ghosts of Departed Quantities; Chapter 5 Curved Space 5.1 Flat Space andMedieval Space5.2 The 2-Sphere and the 3-Sphere; 5.3 Flat Surfaces and the Parallel Axiom; 5.4 The Sphere and the Parallel Axiom; 5.5 Non-Euclidean Geometry; 5.6 Negative Curvature; 5.7 The Hyperbolic Plane; 5.8 Hyperbolic Space; 5.9 Mathematical Space and Actual Space; Chapter 6 The Fourth Dimension; 6.1 Arithmetic of Pairs; 6.2 Searching for an Arithmetic of Triples; 6.3 Why n-tuples Are Unlike Numbers when n ¸ 3; 6.4 Quaternions; 6.5 The Four-Square Theorem; 6.6 Quaternions and Space Rotations; 6.7 Symmetry in Three Dimensions; 6.8 Tetrahedral Symmetry and the 24-Cell 6.9 The Regular PolytopesChapter 7 The Ideal; 7.1 Discovery and Invention; 7.2 Division with Remainder; 7.3 The Euclidean Algorithm; 7.4 Unique Prime Factorization; 7.5 Gaussian Integers; 7.6 Gaussian Primes; 7.7 Rational Slopes and Rational Angles; 7.8 Unique Prime Factorization Lost; 7.9 Ideals-Unique Prime Factorization Regained; Chapter 8 Periodic Space; 8.1 The Impossible Tribar; 8.2 The Cylinder and the Plane; 8.3 Where theWild Things Are; 8.4 PeriodicWorlds; 8.5 Periodicity and Topology; 8.6 A Brief History of Periodicity; 8.7 Non-Euclidean Periodicity; Chapter 9 The Infinite 9.1 Finite and Infinite9.2 Potential and Actual Infinity; 9.3 The Uncountable; 9.4 The Diagonal Argument; 9.5 The Transcendental; 9.6 Yearning for Completeness; Epilogue; References; Index
• Edition: Second edition
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 510; Mathematics Education; Applied Mathematics; Foundations & Theorems; Number Theory; MATHnetBASE; SCI-TECHnetBASE; STMnetBASE; Mathematics -- Study and teaching; Mathematics; Mathematics -- Philosophy; Number theory; Mathematics; Mathematics -- Philosophy; Mathematics -- Study and teaching; Number theory; Electronic books
• Languages: English
• ISBNs: 9780429504815; 0429504810; 9780429998034; 0429998031; 9780429998010; 0429998015; 1138596213; 9781138596214; 9781138586109; 1138586102; 0429998023; 9780429998027
• Related ISBNs: 9781138596214
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.