The Resource Minkowski geometry, A.C. Thompson, (electronic resource)

Minkowski geometry, A.C. Thompson, (electronic resource)

Label
Minkowski geometry
Title
Minkowski geometry
Statement of responsibility
A.C. Thompson
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
The first comprehensive treatment of Minkowski geometry since the 1940's
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1937-
http://library.link/vocab/creatorName
Thompson, Anthony C.
Dewey number
  • 516.3/74
  • 516.374
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA685
LC item number
.T48 1996
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
  • Encyclopedia of mathematics and its applications
  • Encyclopedia of Mathematics and its Applications
Series volume
v. 63
http://library.link/vocab/subjectName
Minkowski geometry
Label
Minkowski geometry, A.C. Thompson, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 313-330) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; CONTENTS; PREFACE; ACKNOWLEDGEMENTS; 0 The algebraic properties of linear spaces and convex sets; 0.1 Linear spaces; 0.2 Convex sets; 0.3 Notes; 1 Norms and norm topologies; 1.1 Norm topologies; 1.2 The unique linear topology on Rd; 1.3 The Hahn-Banach theorem; 1.4 The existence and uniqueness of Haar measure; 1.5 Notes; 2 Convex bodies; 2.1 Separation and support theorems; 2.2 Support functions and polar reciprocals; 2.3 Volumes and mixed volumes; 2.4 Various derived metrics; 2.5 Approximation of convex sets and the Blaschke selection theorem
  • 2.6 Notes3 Comparisons and contrasts with Euclidean space; 3.1 The Mazur-Ulam theorem; 3.2 Normality in Minkowski space; 3.3 The Lowner ellipsoid; 3.4 Characterizations of Euclidean space; 3.5 Notes; 4 Two-dimensional Minkowski spaces; 4.1 Inscribed regular hexagons and other constructions; 4.2 Sets of constant width and equichordal sets; 4.3 Lengths of curves, perimeter of the unit ball; 4.4 The isoperimetric problem in a Minkowski plane; 4.5 Isoperimetric inequalities; 4.6 Transversality; 4.7 Radon curves; 4.8 Notes; 5 The concept of area and content; 5.1 Requirements and examples
  • 6.3 Cauchy's formula for surface areas6.4 Integral geometry in Minkowski spaces; 6.5 Bounds for the surface area of B; 6.6 Miscellaneous properties; 6.7 Notes; 7 Special properties of the Busemann definition; 7.1 The convexity of the area function σ; 7.2 Properties of the mapping I; 7.3 Area and Hausdorff measures; 7.4 Bounds for the surface area of B; 7.5 Notes; 8 Trigonometry; 8.1 The functions cm and sm; 8.2 The function α; 8.3 Trigonometric formulas; 8.4 Differentiation of the trigonometric functions; 8.5 Notes; 9 Various numerical parameters; 9.1 Projection constants
  • 9.2 Macphail's constant9.3 The inner metric; 9.4 The girth, perimeter, inner radius and inner diameter of X; 9.5 Five examples in Rd; 9.6 Relationships with the Banach-Mazur distance and extreme values; 9.7 Notes; 10 Fifty problems; REFERENCES; NOTATION INDEX; AUTHOR INDEX; SUBJECT INDEX
Dimensions
unknown
Extent
1 online resource (366 p.)
Form of item
online
Isbn
9781107091306
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001105884
  • (EBL)1179165
  • (OCoLC)853360459
  • (SSID)ssj0000877425
  • (PQKBManifestationID)11536756
  • (PQKBTitleCode)TC0000877425
  • (PQKBWorkID)10906421
  • (PQKB)10130420
  • (UkCbUP)CR9781107325845
  • (MiAaPQ)EBC1179165
  • (EXLCZ)992550000001105884
Label
Minkowski geometry, A.C. Thompson, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 313-330) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; CONTENTS; PREFACE; ACKNOWLEDGEMENTS; 0 The algebraic properties of linear spaces and convex sets; 0.1 Linear spaces; 0.2 Convex sets; 0.3 Notes; 1 Norms and norm topologies; 1.1 Norm topologies; 1.2 The unique linear topology on Rd; 1.3 The Hahn-Banach theorem; 1.4 The existence and uniqueness of Haar measure; 1.5 Notes; 2 Convex bodies; 2.1 Separation and support theorems; 2.2 Support functions and polar reciprocals; 2.3 Volumes and mixed volumes; 2.4 Various derived metrics; 2.5 Approximation of convex sets and the Blaschke selection theorem
  • 2.6 Notes3 Comparisons and contrasts with Euclidean space; 3.1 The Mazur-Ulam theorem; 3.2 Normality in Minkowski space; 3.3 The Lowner ellipsoid; 3.4 Characterizations of Euclidean space; 3.5 Notes; 4 Two-dimensional Minkowski spaces; 4.1 Inscribed regular hexagons and other constructions; 4.2 Sets of constant width and equichordal sets; 4.3 Lengths of curves, perimeter of the unit ball; 4.4 The isoperimetric problem in a Minkowski plane; 4.5 Isoperimetric inequalities; 4.6 Transversality; 4.7 Radon curves; 4.8 Notes; 5 The concept of area and content; 5.1 Requirements and examples
  • 6.3 Cauchy's formula for surface areas6.4 Integral geometry in Minkowski spaces; 6.5 Bounds for the surface area of B; 6.6 Miscellaneous properties; 6.7 Notes; 7 Special properties of the Busemann definition; 7.1 The convexity of the area function σ; 7.2 Properties of the mapping I; 7.3 Area and Hausdorff measures; 7.4 Bounds for the surface area of B; 7.5 Notes; 8 Trigonometry; 8.1 The functions cm and sm; 8.2 The function α; 8.3 Trigonometric formulas; 8.4 Differentiation of the trigonometric functions; 8.5 Notes; 9 Various numerical parameters; 9.1 Projection constants
  • 9.2 Macphail's constant9.3 The inner metric; 9.4 The girth, perimeter, inner radius and inner diameter of X; 9.5 Five examples in Rd; 9.6 Relationships with the Banach-Mazur distance and extreme values; 9.7 Notes; 10 Fifty problems; REFERENCES; NOTATION INDEX; AUTHOR INDEX; SUBJECT INDEX
Dimensions
unknown
Extent
1 online resource (366 p.)
Form of item
online
Isbn
9781107091306
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001105884
  • (EBL)1179165
  • (OCoLC)853360459
  • (SSID)ssj0000877425
  • (PQKBManifestationID)11536756
  • (PQKBTitleCode)TC0000877425
  • (PQKBWorkID)10906421
  • (PQKB)10130420
  • (UkCbUP)CR9781107325845
  • (MiAaPQ)EBC1179165
  • (EXLCZ)992550000001105884

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