**Description**

The programme contains a visual proof of the fundamental theorem of algebra, mostly shown by using computer graphics.

Module code and title: | M101, Mathematics: a foundation course |
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Item code: | M101; 30 |

First transmission date: | 01-10-1978 |

Published: | 1978 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:25:00 |

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Producer: | John Jaworski |

Contributors: | Colin Rourke; Allan I.,1936-2013 Solomon |

Publisher: | BBC Open University |

Keyword(s): | Animation; Complex numbers; Winding machine; Winding numbers |

Footage description: | The aim of the programme is to prove that any polynomial of degree 'n' has 'n' roots, including polynomials containing complex numbers. Colin Rourke, using computer animations, show how it would be possible to find where a root occurs for a polynominal. This is done by plotting complex numbers, of the same modulus, in the domain to the polynominal function in the codomain. Using this technique, illustrated by computer animations, Colin and Allan Solomon show that every polynominal has a root. A problem arises with this proof when the image curve does not really enclose the origin. To avoid this problem Colin introduces a winding machine which measures true rotations around the origin. The concept of winding numbers is illustrated by computer graphics and then Colin explains how this idea can replace the term "enclose the origin" in the original proof and so make it watertight. Having shown that a polyniminal has at least one root, Allan Solomon now shows algebraically that any polynominal to degree 'n' has 'n' roots. |

Master spool number: | DOU2831 |

Production number: | FOUM430D |

Videofinder number: | 469 |

Available to public: | no |