Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups, or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.
Integral Geometry and Geometric Probability
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Editorial Reviews
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' ... the author handled his material with great dexterity and ease. The book should serve as an excellent text for a graduate course on integral ' Bulletin of the American Mathematical Society
--This text refers to an out of print or unavailable edition of this title.
Book Description
The standard reference in the field, now available in the Cambridge Mathematical Library. Developments in integral geometry have proved to be useful in several fields ranging from pure mathematics to technical and applied disciplines. This book is a systematic exposition of the theory and a compilation of the main results in the field. It can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.
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4.0 out of 5 stars
a treasure trove of material, reprinted,
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This review is from: Integral Geometry and Geometric Probability (Cambridge Mathematical Library) (Kindle Edition)
The exposition is less than perfect, but most people I know working int he area of integral geometery started with this book, and lived happy productive lives as a result. For the longest time out of print, but you don't have to read smudgy photocopies any more. The price is quite reasonable.
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Inside This Book
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First Sentence:
Convex sets play an important role in integral geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geometria integral, kinematic fundamental formula, kinematic density, random great circles, mean curvature integrals, curvatura constante, noneuclidean spaces, invariant density, random tessellations, constant breadth, total absolute curvature, invariant volume element, integral geometry, kinematic formula, geometrical probability, closed convex curve, elliptic space, elliptic plane, kinematic measure, exterior multiplication, needle problem, random inside, bounded convex set, random planes, spherical image Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Some Mean Values, Lattices of Figures New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Convex sets play an important role in integral geometry. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geometria integral, kinematic fundamental formula, kinematic density, random great circles, mean curvature integrals, curvatura constante, noneuclidean spaces, invariant density, random tessellations, constant breadth, total absolute curvature, invariant volume element, integral geometry, kinematic formula, geometrical probability, closed convex curve, elliptic space, elliptic plane, kinematic measure, exterior multiplication, needle problem, random inside, bounded convex set, random planes, spherical image Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Some Mean Values, Lattices of Figures New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 45
books:
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39
books
cite this book:
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- Stochastic Geometry (Wiley Series in Probability & Statistics) by Robert Harding on 8 pages
- Differential Forms (Dover Books on Mathematics) by Henri Cartan on page 147, page 353, and page 357
- Studies in Global Geometry and Analysis by Shiing-Shen Chern in Back Matter (1), Back Matter (2), and Back Matter (3)
- Advanced Calculus, Revised Edition by Loomis in Back Matter (1), and Back Matter (2)
- Random Sets and Integral Geometry (Probability & Mathematical Statistics) by F. Matheron in Back Matter
See all 45 books this book cites
- Integral Geometry And Convexity: Proceedings of the International Conference, Wuhan, China, 18 - 23 October 2004 by Eric L. Grinberg on page 167, page 188, and page 226
- Factorization Calculus and Geometric Probability (Encyclopedia of Mathematics and its Applications) by R. V. Ambartzumian in Front Matter, and Back Matter
- Advances on Theoretical and Methodological Aspects of Probability and Statistics by N. Balakrishnan on page 115
- Introduction to Geometric Probability (Lezioni Lincee) by Daniel A. Klain in Back Matter
- Geometry and Robotics: Workshop, Toulouse, France, May 26-28, 1988. Proceedings (Lecture Notes in Computer Science) by Jean-Daniel Boissonnat on page 205
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