Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Foreword
- Chapter 1 Mamikon's Sweeping Tangent Theorem
- Chapter 2 Cycloids and Trochoids
- Chapter 3 Cyclogons and Trochogons
- Chapter 4 Circumgons and Circumsolids
- Chapter 5 The Method of Punctured Containers
- Chapter 6 Unwrapping Curves from Cylinders and Cones
- Chapter 7 New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors
- Chapter 8 Ellipse to Hyperbola: “With This String I Thee Wed”
- Chapter 9 Trammels
- Chapter 10 Isoperimetric and Isoparametric Problems
- Chapter 11 Arclength and Tanvolutes
- Chapter 12 Centroids
- Chapter 13 New Balancing Principles with Applications
- Chapter 14 Sums of Squares
- Chapter 15 Appendix
- Bibliography
- Index
- About the Authors
About the Authors
- Frontmatter
- Contents
- Preface
- Introduction
- Foreword
- Chapter 1 Mamikon's Sweeping Tangent Theorem
- Chapter 2 Cycloids and Trochoids
- Chapter 3 Cyclogons and Trochogons
- Chapter 4 Circumgons and Circumsolids
- Chapter 5 The Method of Punctured Containers
- Chapter 6 Unwrapping Curves from Cylinders and Cones
- Chapter 7 New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors
- Chapter 8 Ellipse to Hyperbola: “With This String I Thee Wed”
- Chapter 9 Trammels
- Chapter 10 Isoperimetric and Isoparametric Problems
- Chapter 11 Arclength and Tanvolutes
- Chapter 12 Centroids
- Chapter 13 New Balancing Principles with Applications
- Chapter 14 Sums of Squares
- Chapter 15 Appendix
- Bibliography
- Index
- About the Authors
Summary
Tom M. Apostol joined the Caltech faculty in 1950 and is Professor of Mathematics, Emeritus. He is internationally known for his books on Calculus, Analysis, and Analytic Number Theory, (translated into 7 languages), and for creating Project MATHEMATICS!, a video series that brings mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international festivals, and were translated into Hebrew, Portuguese, French, and Spanish. Apostol has published 102 research papers, has written two chapters for the Digital Library of Mathematical Functions (2010), and is coauthor of three texts for the physics telecourse: The Mechanical Universe … and Beyond.
He has received several awards for research and teaching. In 1978 he was a visiting professor at the University of Patras, Greece, and in 2001 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek. In 2012 he was selected to be a Fellow of the American Mathematical Society.
Mamikon A. Mnatsakanian was Professor of Astrophysics at Yerevan State University and Director of the Mathematical Modeling Center of Physical Processes, Armenian Academy of Sciences. As an undergraduate he invented ‘Visual Calculus’, more fully described in this book. As an astrophysicist he developed a generalized theory of relativity with variable gravitational constant that resolves observational controversies in Cosmology. He also developed new methods that he applied to radiation transfer theory and to stellar statistics and dynamics.
- Type
- Chapter
- Information
- New Horizons in Geometry , pp. 513Publisher: Mathematical Association of AmericaPrint publication year: 2012