Available online
Description
This programme develops a rigorous definition of winding number.
This programme develops a rigorous definition of winding number.
| 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 |
| + Show more... | |
| 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 |
