《積分幾何與幾何概論》2009年5月世界圖書出版公司出版的圖書，作者是(阿根廷)路易斯桑塔洛。
基本介紹
- 書名：積分幾何與幾何概論
- 作者：(阿根廷)路易斯桑塔洛
- 出版社：世界圖書出版公司
- 出版時間：2009年5月
- ISBN：9787510004933
內容簡介,目錄,
內容簡介
Thoughitstitle"IntegralGeometry"mayappearsomewhatunusualinthiscontextitisneverthelessquiteappropriate,forIntegralGeometryisanoutgrowthofwhatintheoldendayswasreferredtoas"geometricprobabil-ities."Originating,aslegendhasit,withtheBuffonneedleproblem(whichafternearlytwocenturieshaslostlittleofitseleganceandappeal),geometricprobabilitieshaverunintodifficultiesculminatingintheparadoxesofBertrandwhichthreatenedthefledglingfieldwithbanishmentfromthehomeofMathematics.Inrescuingitfromthisfate,Poincar6madethesuggestionthatthearbitrarinessofdefinitionunderlyingtheparadoxescouldberemovedbytyingcloserthedefinitionofprobabilitywithageometricgroupofwhichitwouldhavetobeaninvariant.
目錄
Editor's Statement
Foreword
Preface
Part Ⅰ.INTEGRAL GEOMETRY IN THE PLANE
Chapter 1.Convex Sets in the Plane
Chapter 2.Sets of Points and Poisson Processes in the Plane
Chapter 3.Sets of Lines in the Plane
Chatper 4.Pairs of Points and Pairs of Lines
Chapter 5.Sets of Strips in the Plane
Chapter 6.The Group of Motions in the Plane:Kinematic Density
Chapter 7.Fundamental Formulas of Poincare and Blaschke
Chapter 8.Lattices of Figures
Part Ⅱ.GENERAL INTEGRAL GEOMETRY
Chapter 9.Differential Forms and Lie Groups
Chapter 10.Density and Measure in Homogeneous Spaces
Chapter 11.The Affine Groups
Chpater 12.The Group of Motions in En
Part Ⅲ.INTEGRAL GEOMETRY IN En
Chapter 13.Convex Sets in En
Chapter 14.Linear Subspaces,Convex Sets,and Compact Manifolds
Chapter 15.The Kinematic Density in En
Chpater 16.Geometric and Statistical Applications; Stereology
Part Ⅳ.INTEGRAL GEOMETRY IN SPACES OF CONSTANT CURVATURE
Chapter 17.Noneuclidean Integral Geometry
Chapter 18.Crofton's Formulas and the Kinematic FundaⅠmental Formula in Noneuclidean Spaces
Chapter 19.Integral Geometry and Foliated Spaces; Trends in Integral Geometry
Appendix.Differential Forms and Exterior Calculus
Bibliography and References
Author Index
Subject Index
