Tom Apostol e Mamikon Mnatsakania
The Mathematical Association of America | 2013 | 528 páginas | rar - pdf | 5 Mb
link (password: matav)
New Horizons in Geometry represents the fruits of 15 years of work in geometry by a remarkable team of prize-winning authors Tom Apostol and Mamikon Mnatsakanian. It serves as a capstone to an amazing collaboration. Apostol and Mamikon provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results, the majority of which are new, and frequently develop extensions of familiar theorems that are often surprising and sometimes astounding. It is mathematical exposition of the highest order.
The hundreds of full color illustrations by Mamikon are visually enticing and provide great motivation to read further and savor the wonderful results. Lengths, areas, and volumes of curves, surfaces, and solids are explored from a visually captivating perspective. It is an understatement to say that Apostol and Mamikon have breathed new life into geometry.
CONTENTS
Preface . ix
Introduction . . xi
Foreword . . xiii
Chapter 1. Mamikon’s Sweeping Tangent Theorem . . 1
Chapter 2. Cycloids and Trochoids . . 31
Chapter 3. Cyclogons and Trochogons . . 65
Chapter 4. Circumgons and Circumsolids . . 101
Chapter 5. The Method of Punctured Containers. . 135
Chapter 6. Unwrapping Curves from Cylinders and Cones . . 169
Chapter 7. New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors . 213
Chapter 8. Ellipse to Hyperbola: “With This String I Thee Wed” . . 243
Chapter 9. Trammels . . 267
Chapter 10. Isoperimetric and Isoparametric Problems . . 295
Chapter 11. Arclength and Tanvolutes 331
Chapter 12. Centroids . . 375
Chapter 13. New Balancing Principles with Applications . . 401
Chapter 14. Sums of Squares. . 443
Chapter 15. Appendix . . 473
Sem comentários:
Enviar um comentário