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This programme uses various models to analyse the projective plane RP2 topologically and to interpret some ideas topologically.
Metadata describing this Open University video programme
Module code and title: M335, Studies in pure mathematics
Item code: M335; 03
First transmission date: 17-04-1983
Published: 1983
Rights Statement:
Restrictions on use:
Duration: 00:22:48
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Producer: Jack Koumi
Contributors: David Crowe; Colin Rourke
Publisher: BBC Open University
Keyword(s): Disc; Mobius band; Projective geometry; Projective line; Projective plane
Footage description: Colin Rourke briefly introduces the programme. David Cross, with the aid of still graphics, reviews the geometer's definition of the projective plane. A projective ray model and a geometers plane model are also used to illustrate his points. In order to connect the geometer's description of the projective plane with the topologist's model, Colin Rourke looks at a sphere where imaginary ideal points don't need to be invented. Rourke works with the sphere to move closer to the topologist's projective plane. David Crowe and then Colin Rourke summarise the discussion so far. Graphics diagram and several models are used to show the connection between the geometer's and the topologist's projective planes. Colin Rourke next looks at a spherical model which contains a Mobius band in order to study some topological features of the projective plane. He points out that the cylindrical region around a sphere is, in fact, a Mobius band in the projective plane. Having shown that the projective plane of the cylindrical region around a sphere is nonorientable, Rourke goes on to determine what the rest of the sphere is topologically. He uses models and diagrams of Mobius bands to illustrate his points. David Crowe looks at some further ideas from projective geometry and interprets them topologically. Colin Rourke joins in. They both use the geometers plane model and a spherical model with a plane through its centre. To end the programme, David Crowe and Colin Rourke take the topological ideas introduced in the programme and interpret them on the geometer's plane. Drawing board diagrams, animations and models illustrate their points.
Master spool number: HOU4006
Production number: FOUM132L
Videofinder number: 975
Available to public: no