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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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Autor principal: Roe, John
Lenguaje:eng
Publicado: American Mathematical Society 2015
Materias:
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
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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