**Description**

In 1842 William Rowan Hamilton discovered quaternions. Quaternions are a four dimensional complex number in the form a + bi + cj + dk where i, j and k are distinct square roots of -1. The algebra o...f quaternions, unlike the known algebras of the day, broke the commutative law, and as such it brought about a revolutionary change in mathematical thinking at that time. This film Is an account of the discovery beginning with Hamilton's interpretation of complex numbers, and the problems he faced in trying to generalise them to three dimensions. The programme shows how the breakthrough came by the invention of i, j and k, separate square roots of -1 which had cyclical multiplication properties: ij = k, jk = 1, and ki = j, which gave the famous rule ijk = -1. The film was shot on location in Dublin with Graham Flegg, Chairman of the History of Mathematics Course Team, telling the story from places of historical interest that relate to Hamilton. Dr. A. J. McConnell, Past Provost and Past Professor of Mathematics at Trinity College, Dublin, who has made a special study of Hamilton and his work, gives an account of Hamilton as a person, and the impact of the discovery of quaternions. The film includes many graphic sequences to illustrate the historical background and mathematical development.

Module code and title: | AM289, History of mathematics |
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Item code: | AM289; 09 |

First transmission date: | 08-08-1976 |

Published: | 1976 |

Rights Statement: | Rights owned or controlled by The Open University |

Restrictions on use: | This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OU Digital Archive web pages. |

Duration: | 00:24:30 |

+ Show more... | |

Producer: | John Richmond |

Contributors: | Graham Flegg; A. J. McConnell |

Publisher: | BBC Open University |

Keyword(s): | Algebra; Argand; Hamilton; Quaternions |

Footage description: | Graham Flegg, at Brougham Bridge near Dublin, introduces the programme. A.J. McConnell briefly points out the importance of the discovery of quaternions by Hamilton. Bust of Hamilton. Graham Flegg traces the interest, in Europe and Britain, in complex numbers which served as the background to Hamilton's work on quaternions. Flegg looks particularly at Argand's work on representing complex numbers geometrically. Several animations are used to illustrate points made. A. J. McConnell explains how Hamilton defined the addition and multiplication of numbered pairs. He gives, as an example of Hamilton's system. the equation x2 = -1. Animations illustrate points made. Graham Flegg, outside Trinity College Dublin, discusses the state of European and British mathematics during the 18th century. Stills of Leibniz, Bernoulli brothers, D'Alembert, Euler, Gauss and Argand. Graham Flegg goes on to discuss, briefly, the revival of British mathematics, particularly the interest in algebra, during the 19th century. A. J. McConnell gives a brief biographical sketch of Hamilton. Graham Flegg joins in. Bust of Hamilton, still of the Dunsink Observatory and pan along the observatory gardens. A.J. McConnell explains how Hamilton tried to extend his number pairs to number triplets. Several animations are used to illustrate points Graham Flegg joins in to point out how Peacock's "Principle of Equivalent Forms" inhibited Hamilton's work on number triplets for several years. McConnell explains how Hamilton finally solved the problem of developing an algebra of quaternions which satisfies all the laws of algebra except the commutative law. Several animations illustrate the points. Graham Flegg introduces a long quote from Hamilton in which he describes his discovery of quaternions. Quote from Hamilton over shots of canal and Brougham Bridge. McConnell and Flegg sum up. |

Master spool number: | 6HT/72121 |

Production number: | 00525_3183 |

Videofinder number: | 944 |

Available to public: | no |