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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...
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Lenguaje: | eng |
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American Mathematical Society
2015
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Acceso en línea: | http://cds.cern.ch/record/2264092 |
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author | Roe, John |
author_facet | Roe, John |
author_sort | Roe, John |
collection | CERN |
description | 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 |
id | cern-2264092 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2015 |
publisher | American Mathematical Society |
record_format | invenio |
spelling | cern-22640922021-04-21T19:13:49Zhttp://cds.cern.ch/record/2264092engRoe, JohnWinding around: the winding number in topology, geometry, and analysisMathematical Physics and MathematicsThe 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 everAmerican Mathematical Societyoai:cds.cern.ch:22640922015 |
spellingShingle | Mathematical Physics and Mathematics Roe, John Winding around: the winding number in topology, geometry, and analysis |
title | Winding around: the winding number in topology, geometry, and analysis |
title_full | Winding around: the winding number in topology, geometry, and analysis |
title_fullStr | Winding around: the winding number in topology, geometry, and analysis |
title_full_unstemmed | Winding around: the winding number in topology, geometry, and analysis |
title_short | Winding around: the winding number in topology, geometry, and analysis |
title_sort | winding around: the winding number in topology, geometry, and analysis |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/2264092 |
work_keys_str_mv | AT roejohn windingaroundthewindingnumberintopologygeometryandanalysis |