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Description
This programme investigates the idea of symmetry of three-dimensional objects, and develops a strategy for counting the symmetries of five so-called 'Platonic Solids'.
This programme investigates the idea of symmetry of three-dimensional objects, and develops a strategy for counting the symmetries of five so-called 'Platonic Solids'.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 02C; 1995 |
| First transmission date: | 1994 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:21 |
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| Producer: | Andrew Adamyk |
| Contributors: | David Brannan; Pip Surgey |
| Publisher: | BBC Open University |
| Keyword(s): | Cayley Table; Equilateral Triangle; Geometry; Groups |
| Subject terms: | Geometry; Symmetry |
| Footage description: | The programme begins by introducing the idea of symmetry of three-dimensional objects. David Brannan illustrates this idea using objects that can be found in the kitchen of an average house. David also introduces five symmetrical objects of special importance the so called "Platonic Solids"- The problem is posed of counting the symmetries of these solids, in particular the tetrahedron. Next, Pip Surgey presents a review of what is known about the symmetry of two dimensional figures, using as an example the equilateral triangle. The six symmetries of the equilateral triangle are identified and split into two sets: three "direct" symmetries (rotations) and three "indirect" ones (reflections). An algebraic notation is developed to describe these symmetries and a Cayley table is used to record their composites. David Brannan continues by identifying the twenty four symmetries of the tetrahedron. He finds nine direct symmetries without difficulty and then a further three by composing the ones he's already found. He identifies one indirect symmetry and then finds a further eleven by following it by each direct symmetry in turn. Pip now gives a strategy for counting the symmetries of any platonic solid. And finally David uses this strategy to check his result for the tetrahedron. |
| Master spool number: | DOU8008 |
| Production number: | FOUM467K |
| Videofinder number: | 3290 |
| Available to public: | no |
