Available online
Description
This programme shows how inverse geometry can be used to study the geometry of circles.
This programme shows how inverse geometry can be used to study the geometry of circles.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 02E |
| First transmission date: | 1995 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:05 |
| + Show more... | |
| Producer: | Andrew Adamyk |
| Contributors: | Judith Daniels; Jeremy Gray |
| Publisher: | BBC Open University |
| Keyword(s): | Circles of Apollonius; Generalised circle; Geometry; Inversion; Line; Reflection; Straight line |
| Subject terms: | Geometry, Algebraic; Inversions |
| Footage description: | In this programme we introduce the idea of inversive geometry, and show how it can be used to study the geometry of circles. The programme is in four sections, intended to form the basis of four video bands in possible future use. In the first section we introduce a transformation called inversion, and show how it can be considered as a generalisation of reflection in a straight line. In the second section of the programme we investigate the basic properties of inversion, and in particular its effect on lines and circles. We show that inversion blurs the distinction between straight lines and circles, and introduce the idea of a generalised circle to include both lines and circles. In the third section we show how you can use inversion to solve some tricky problems involving circles. In the final section of the programme we use inversion to explore the Circles of Apollonius, which were introdcued at the beginning of the Geometry block of M203. |
| Master spool number: | DOU7646 |
| Production number: | FOUM420L |
| Videofinder number: | 4644 |
| Available to public: | no |
