**Description**

This programme explains the idea of classification using equivalence relations using examples from geometry.

Module code and title: | M101, Mathematics: a foundation course |
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Item code: | M101; 29; 1986 |

First transmission date: | 14-09-1986 |

Published: | 1986 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:24:45 |

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Producer: | David Saunders |

Contributors: | Bob Coates; Allan I.,1936-2013 Solomon; Bob Margolis |

Publisher: | BBC Open University |

Keyword(s): | Area; Euclidean congruences; Geometry; Hyperbolas; Matrix transformations; Triangles |

Footage description: | This programme explains the idea of classification using equivalence relations (introduced in section 2 of the unit) using examples from geometry. The programme starts by posing a problem involving the areas of two triangles; although there is a straightforward but lengthy way of solving the problems using calculation, the ideas about to be introduced provide a much simpler solution. These ideas are explained by looking first at the symmetries of a given equilateral triangle, and asking how the points of the plane can be classified using these symmetries. A computer animation shows that in general there are sets containing six equivalent points, where each point is related to any other by either a reflection or a rotation which preserves the triangle. The programme explains that such a relation is characterised by the properties of being symmetric, reflexive, and transitive, and is called an equivalence relation. Students are then reminded of a problem involving matrices from the television section of the text, and are shown the strategy for proving that the relation so defined is actually an equivalence relation; computer animation demonstrates that the corresponding sets of equivalent points are concentric circles. It is explained that the matrix transformations - rotations - are special cases of Euclidean congruencies, and in fact a rotation can be used to give a simple solution to the problem from the beginning of the programme. Finally, students are posed a further problem involving matrix transformations which give rise to hyperbolas rather than circles. |

Master spool number: | HOU5543 |

Production number: | FOUM258K |

Videofinder number: | 2491 |

Available to public: | no |