Available online
Description
This programme shows how theorem-proving becomes easier when geometers haver access to affine geometry.
This programme shows how theorem-proving becomes easier when geometers haver access to affine geometry.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 01E; 1995 |
| First transmission date: | 1995 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:02 |
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| Producer: | Andrew Adamyk |
| Contributors: | Lynne Burrell; Jeremy Gray |
| Publisher: | BBC Open University |
| Keyword(s): | Affine geometry/transformation; Circle; Conjugate diameters; Ellipse; Linear transformation; Midpoint theorem; Parallel projection; Shadow; Sunlight |
| Subject terms: | Geometry, Affine |
| Footage description: | In this programme we introduce the idea of affine geometry and look at different aspects of its use. The programme is in three sections, intended to form the basis of three video bands in possible future use. In the first section we introduce two theorems about ellipses; the midpoint theorem and the conjugate diameters theorem. We show how these theorems are straightforward to prove for the special case when the ellipse is a circle. We show how we could prove the theorems in the general case by transforming an ellipse into a circle. In the second section of the programme we investigate a transformation know as parallel projection, which formalises the ideas of shadows cast by sunlight. We show how this transformation has exactly the properties we need to map circles into ellipses. In the final section of the programme we show how parallel projection is only one of a new class of transformations called affine transformations. We investigate the algebra of affine transformations, and show that any affine transformation can be realised as a series of parallel projections. |
| Master spool number: | DOU7616 |
| Production number: | FOUM416K |
| Videofinder number: | 4643 |
| Available to public: | no |
