Softcover ISBN:  9781470469597 
Product Code:  STML/96 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470470364 
Product Code:  STML/96.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470469597 
eBook: ISBN:  9781470470364 
Product Code:  STML/96.B 
List Price:  $118.00 $88.50 
Softcover ISBN:  9781470469597 
Product Code:  STML/96 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470470364 
Product Code:  STML/96.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470469597 
eBook ISBN:  9781470470364 
Product Code:  STML/96.B 
List Price:  $118.00 $88.50 

Book DetailsStudent Mathematical LibraryVolume: 96; 2022; 416 ppMSC: Primary 53
This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way.
After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the fourvertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curveshortening flow that is based on original articles but requires a minimum of previous knowledge.
Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
ReadershipUndergraduate and graduate students interested in curves in the Euclidean plane.

Table of Contents

Chapters

Plane curves

Winding number

Rotation index

Jordan curve theorem

Isoperimetric inequality

Convex curves

The fourvertex theorem

Curveshortening flow

Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curveshortening flow

Appendix B. Answers to selected exercises


Additional Material

Reviews

The authors focus their attention on the differential geometry of planar curves with great depth, although phenomenal books on differential geometry already exist. Many interesting and inspiring geometrical and topological results on planar curves are here presented in an elementary form. The topics are chosen to sharpen the reader's mathematical intuition for asserted geometric concepts and results. A very good selection of examples guides the reader towards a better understanding of each notion.
Ergin Bayram (Samsun)


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way.
After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the fourvertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curveshortening flow that is based on original articles but requires a minimum of previous knowledge.
Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.
Undergraduate and graduate students interested in curves in the Euclidean plane.

Chapters

Plane curves

Winding number

Rotation index

Jordan curve theorem

Isoperimetric inequality

Convex curves

The fourvertex theorem

Curveshortening flow

Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curveshortening flow

Appendix B. Answers to selected exercises

The authors focus their attention on the differential geometry of planar curves with great depth, although phenomenal books on differential geometry already exist. Many interesting and inspiring geometrical and topological results on planar curves are here presented in an elementary form. The topics are chosen to sharpen the reader's mathematical intuition for asserted geometric concepts and results. A very good selection of examples guides the reader towards a better understanding of each notion.
Ergin Bayram (Samsun)