Available online
Description
This programme attempts to explain the mathematical induction process. Several examples of proofs are demonstrated.
This programme attempts to explain the mathematical induction process. Several examples of proofs are demonstrated.
| Module code and title: | M101, Mathematics: a foundation course |
|---|---|
| Item code: | M101; 05; 1978 |
| First transmission date: | 12-03-1978 |
| Published: | 1978 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:23:18 |
| + Show more... | |
| Producer: | David Saunders |
| Contributors: | Norman Gowar; John Mason |
| Publisher: | BBC Open University |
| Keyword(s): | Cubes; Induction; Polygon interior angles; Positive integers |
| Footage description: | The aims of this programme are to illustrate the idea of mathematical induction, and to show how induction can be used to prove results about positive integers. The programme starts with the problem of finding the sum of the first n cubes. To calculate this for a given number of cubes is straightforward although tedious, but a general formula is much more difficult to find. An analogy is provided by an example from the text, finding the sum of the first in positive integers. But even with a general formula, how can the result be proved? The method of proof called mathematical induction is shown visually as a sequence of stitches in a seam, breaking one after the other. The principle behind this illustration is used to prove two simple results about the divisibility of numbers specified by formulae, and is then used to solve the original problem of the sum of cubes. Finally another problem, concerning the interior angles of a polygon, is left for the student to solve. |
| Master spool number: | 6HT/72359 |
| Production number: | 00525_4242 |
| Videofinder number: | 2453 |
| Available to public: | no |
