Cargando…
Winding around: the winding number in topology, geometry, and analysis
The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has fa...
Autor principal: | |
---|---|
Lenguaje: | eng |
Publicado: |
American Mathematical Society
2015
|
Materias: | |
Acceso en línea: | http://cds.cern.ch/record/2264092 |
Sumario: | The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra), guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem), explain why ever |
---|