Geometric Tomography
eBook - PDF

Geometric Tomography

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Geometric Tomography

About this book

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although primarily meant for researchers and graduate students in geometry and tomography, brief introductions, suitable for advanced undergraduates, are provided to the basic concepts. More than 70 illustrations are used to clarify the text. The book also presents 66 unsolved problems. Each chapter ends with extensive notes, historical remarks, and some biographies. This edition includes numerous updates and improvements, with some 300 new references bringing the total to over 800.

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Yes, you can access Geometric Tomography by Richard J. Gardner in PDF and/or ePUB format, as well as other popular books in Matemáticas & Análisis matemático. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Series Page
  3. Title
  4. Copyright
  5. Dedication
  6. CONTENTS
  7. PREFACE TO THE SECOND EDITION
  8. PREFACE
  9. 0 Background material
  10. 1 Parallel X-rays of planar convex bodies
  11. 2 Parallel X-rays in n dimensions
  12. 3 Projections and projection functions
  13. 4 Projection bodies and volume inequalities
  14. 5 Point X-rays
  15. 6 Chord functions and equichordal problems
  16. 7 Sections, section functions, and point X-rays
  17. 8 Intersection bodies and volume inequalities
  18. 9 Estimates from projection and section functions
  19. Appendix A Mixed volumes and dual mixed volumes
  20. Appendix B Inequalities
  21. Appendix C Integral transforms
  22. REFERENCES
  23. NOTATION
  24. AUTHOR INDEX
  25. SUBJECT INDEX