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This programme develops a rigorous definition of winding number.
Metadata describing this Open University video programme
Module code and title: M335, Studies in pure mathematics
Item code: M335; 07
First transmission date: 07-08-1983
Published: 1983
Rights Statement:
Restrictions on use:
Duration: 00:24:00
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Producer: Jack Koumi
Contributors: John Peters; Colin Rourke
Publisher: BBC Open University
Keyword(s): Brouwer degree; Homotopy; Loop; Winding number
Footage description: The winding number of a loop about a point is "the number" of times the loop circles the point. This number depends on the position of the point and the nature of the loop. For example, the loop may intersect itself several times. The first part of the programme uses studio models, diagrams and animations to develop a rigorous definition of winding number. The definition is in terms of a continuous function from an interval to an infinite spiral sitting above the loop. Further diagrams and animations show what's meant by a "continuous deformation" (a "homotopy") of a loop and how this affects the winding number. Finally, there's an intriguing application to the study of continuous functions: the idea of winding number can be used to classify them according to their "Brouwer Degree". This classification gives a deep insight into the nature of the function.
Master spool number: HOU4207
Production number: FOUM153N
Videofinder number: 979
Available to public: no