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 four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening 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.

About the Author
Hilario Alencar, Federal University of Alagoas, Maceio, Alagoas, Brazil.

Walcy Santos, Federal University of Rio de Janeiro, Brazil.

Gregorio Silva Neto, Universidade Federal de Alagoas, Maceio, Alagoas, Brazil.


Book Information
ISBN 9781470469597
Author Hilario Alencar
Format Paperback
Page Count 416
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 512g