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The Resource Yearning for the impossible : the surprising truths of mathematics, John Stillwell

Yearning for the impossible : the surprising truths of mathematics, John Stillwell

Label
Yearning for the impossible : the surprising truths of mathematics
Title
Yearning for the impossible
Title remainder
the surprising truths of mathematics
Statement of responsibility
John Stillwell
Creator
Subject
Language
eng
Cataloging source
DLC
http://library.link/vocab/creatorName
Stillwell, John
Illustrations
illustrations
Index
index present
LC call number
QA37.3
LC item number
.S75 2006
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematics
  • Recreações matemáticas
  • Mathematik
Label
Yearning for the impossible : the surprising truths of mathematics, John Stillwell
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 215-217) and index
Contents
  • Irrational triangles
  • 1.4.
  • The Pythagorean nightmare
  • 1.5.
  • Explaining the irrational
  • 1.6.
  • The continued fraction for [square root of] 2
  • 1.7.
  • Equal temperament
  • 2.
  • Preface
  • The imaginary
  • Negative numbers
  • Imaginary numbers
  • Solving cubic equations
  • 2.4.
  • Real solutions via imaginary numbers
  • 2.5.
  • Where were imaginary numbers before 1572?
  • 2.6.
  • Geometry of multiplication
  • 1.
  • 2. 7.
  • Complex numbers give more than we aked for
  • 2.8.
  • Why call them "complex" numbers?
  • 3.
  • The horizon
  • 3.1.
  • Parallel lines
  • 3.2.
  • Coordinates
  • The irrational
  • 3.3
  • Parallel lines and vision
  • 3.4.
  • Drawing without measurement
  • 3.5.
  • The theorems of Pappus and Desargues
  • 3.6.
  • The little Desargues theorem
  • What are the laws of algebra?
  • 3.8.
  • 1.1.
  • Projective addition and multiplication
  • 4.
  • The infinitesimal
  • 4.1.
  • Length and area
  • 4.2.
  • Volume
  • 4.3.
  • Volume of a tetrahedron
  • 4.4.
  • The Pythagorean dream
  • The circle
  • 4.5.
  • The parabola
  • 4.6.
  • The slopes of other curves
  • 4.7.
  • Slope and area
  • 4.8.
  • The value of [pi]
  • 4.9.
  • 1.2.
  • Ghosts of departed quantities
  • The Pythagorean theorem
  • 1.3.
  • 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.
  • 5.9.
  • Mathematical space and actual space
  • 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 [is greater than or equal to] 3
  • Curved space
  • 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
  • 5.1.
  • 6.9
  • The regular polytopes
  • 7.
  • The ideal
  • 7.1.
  • Discovery and invention
  • 7.2.
  • Division with remainder
  • 7.3.
  • Unique prime factorization
  • Flat space and medieval space
  • 7.4.
  • Gaussian integers
  • 7.5.
  • Gaussian primes
  • 7.6.
  • Rational slopes and rational angles
  • 7.7.
  • Unique prime factorization lost
  • 7.8.
  • Ideals, or unique prime factorization regained
  • 5.2.
  • The 2-sphere and the 3-sphere
  • 5.3.
  • Flat surfaces and the parallel axiom
  • 8.4.
  • Periodic worlds
  • 8.5.
  • Periodicity and topology
  • 8.6.
  • A brief history of periodicity
  • 9.
  • The infinite
  • 9.1.
  • Finite and infinite
  • 8.
  • 9.2.
  • Potential and actual infinity
  • 9.3.
  • The uncountable
  • 9.4.
  • The diagonal argument
  • 9.5.
  • The transcendental
  • 9.6.
  • Yearning for completeness
  • Periodic space
  • Epilogue
  • Index
  • 8.1.
  • The impossible tribar
  • 8.2.
  • The cylinder and the plane
  • 8.3.
  • Where the wild things are
Control code
62093052
Dimensions
24 cm
Extent
xiii, 230 p.
Isbn
9781568812540
Isbn Type
(alk. : paper)
Lccn
2005054950
Other physical details
ill.
System control number
(OCoLC)62093052
Label
Yearning for the impossible : the surprising truths of mathematics, John Stillwell
Publication
Bibliography note
Includes bibliographical references (p. 215-217) and index
Contents
  • Irrational triangles
  • 1.4.
  • The Pythagorean nightmare
  • 1.5.
  • Explaining the irrational
  • 1.6.
  • The continued fraction for [square root of] 2
  • 1.7.
  • Equal temperament
  • 2.
  • Preface
  • The imaginary
  • Negative numbers
  • Imaginary numbers
  • Solving cubic equations
  • 2.4.
  • Real solutions via imaginary numbers
  • 2.5.
  • Where were imaginary numbers before 1572?
  • 2.6.
  • Geometry of multiplication
  • 1.
  • 2. 7.
  • Complex numbers give more than we aked for
  • 2.8.
  • Why call them "complex" numbers?
  • 3.
  • The horizon
  • 3.1.
  • Parallel lines
  • 3.2.
  • Coordinates
  • The irrational
  • 3.3
  • Parallel lines and vision
  • 3.4.
  • Drawing without measurement
  • 3.5.
  • The theorems of Pappus and Desargues
  • 3.6.
  • The little Desargues theorem
  • What are the laws of algebra?
  • 3.8.
  • 1.1.
  • Projective addition and multiplication
  • 4.
  • The infinitesimal
  • 4.1.
  • Length and area
  • 4.2.
  • Volume
  • 4.3.
  • Volume of a tetrahedron
  • 4.4.
  • The Pythagorean dream
  • The circle
  • 4.5.
  • The parabola
  • 4.6.
  • The slopes of other curves
  • 4.7.
  • Slope and area
  • 4.8.
  • The value of [pi]
  • 4.9.
  • 1.2.
  • Ghosts of departed quantities
  • The Pythagorean theorem
  • 1.3.
  • 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.
  • 5.9.
  • Mathematical space and actual space
  • 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 [is greater than or equal to] 3
  • Curved space
  • 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
  • 5.1.
  • 6.9
  • The regular polytopes
  • 7.
  • The ideal
  • 7.1.
  • Discovery and invention
  • 7.2.
  • Division with remainder
  • 7.3.
  • Unique prime factorization
  • Flat space and medieval space
  • 7.4.
  • Gaussian integers
  • 7.5.
  • Gaussian primes
  • 7.6.
  • Rational slopes and rational angles
  • 7.7.
  • Unique prime factorization lost
  • 7.8.
  • Ideals, or unique prime factorization regained
  • 5.2.
  • The 2-sphere and the 3-sphere
  • 5.3.
  • Flat surfaces and the parallel axiom
  • 8.4.
  • Periodic worlds
  • 8.5.
  • Periodicity and topology
  • 8.6.
  • A brief history of periodicity
  • 9.
  • The infinite
  • 9.1.
  • Finite and infinite
  • 8.
  • 9.2.
  • Potential and actual infinity
  • 9.3.
  • The uncountable
  • 9.4.
  • The diagonal argument
  • 9.5.
  • The transcendental
  • 9.6.
  • Yearning for completeness
  • Periodic space
  • Epilogue
  • Index
  • 8.1.
  • The impossible tribar
  • 8.2.
  • The cylinder and the plane
  • 8.3.
  • Where the wild things are
Control code
62093052
Dimensions
24 cm
Extent
xiii, 230 p.
Isbn
9781568812540
Isbn Type
(alk. : paper)
Lccn
2005054950
Other physical details
ill.
System control number
(OCoLC)62093052

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      32.771354 -117.193327
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