rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Yearning for the Impossible
    sub title: the Surprising Truths of Mathematics, Second Edition
  name:
    name part: Stillwell, John
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  genre: History
  origin info:
    place:
      place term: flu
    date issued: 2018
    edition: Second edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource : text file, PDF
  abstract: "Yearning for the Impossible: The Surprising Truth of Mathematics, Second Edition explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress. The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. This new edition contains many new exercises and commentaries, clearly discussing a wide range of challenging subjects."--Provided by publisher.
  table of 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.
  table of contents: 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 ơ; 4.9 Ghosts of Departed Quantities; Chapter 5 Curved Space.
  table of contents: 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 ı 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.
  table of contents: 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.
  table of contents: 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.
  note: John Stillwell.
  note: Includes bibliographical references and index.
  subject:
    topic: Mathematics
    topic: Study and teaching
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics
    topic: Philosophy
  subject:
    topic: Number theory
  subject:
    topic: Mathematics
  subject:
    topic: Mathématiques
    topic: Étude et enseignement
  subject:
    topic: Mathématiques
  subject:
    topic: Mathématiques
    topic: Philosophie
  subject:
    topic: Théorie des nombres
  subject:
    topic: MATHEMATICS
    topic: Essays
  subject:
    topic: MATHEMATICS
    topic: Pre-Calculus
  subject:
    topic: MATHEMATICS
    topic: Reference
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics
    topic: Philosophy
  subject:
    topic: Mathematics
    topic: Study and teaching
  subject:
    topic: Number theory
  classification: QA37.3 .S755 2018
  identifier: 9780429504815
  identifier: 0429504810
  identifier: 9780429998034
  identifier: 0429998031
  identifier: 9780429998010
  identifier: 0429998015
  identifier: 1138596213
  identifier: 9781138596214
  identifier: 9781138586109
  identifier: 1138586102
  identifier: 0429998023
  identifier: 9780429998027
  identifier: 9780429998027 Ingram Content Group
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: CRCPR
    record creation date: 180413
    record change date: 20241111204747.8
    record identifier: in00005528091
    language of cataloging:
      language term: eng