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This programme defines the concept of orientability and uses a variety of animations and models to show that every non-orientable surface must contain a Mobius band.
Metadata describing this Open University video programme
Module code and title: M335, Studies in pure mathematics
Item code: M335; 02
First transmission date: 13-03-1983
Published: 1983
Rights Statement:
Restrictions on use:
Duration: 00:23:50
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Producer: Jack Koumi
Contributors: Jeremy Gray; Colin Rourke
Publisher: BBC Open University
Keyword(s): Mobius band; Orientable
Footage description: Colin Rourke introduces the programme by demonstrating some differences between a cylinder and a Mobius band. Jeremy Gray points out, with the aid of animated diagrams, an additional property which distinguishes the Mobius band from the cylinder, that of orientability. Shots of models of Mobius bands. Gray goes on to look at another non-orientable surface, that of two Mobius bands joined together. A series of orientable surfaces (cylinder sphere and disc) are examined in order to reinforce the idea of orientability and how this is applied to any surface. With the aid of animated diagrams and models a rule for orientability is established and tested on several surfaces. Colin Rourke points out that when this rule is applied to a Mobius band it is found to be non-orientable. Gray explains why a theorem which shows that any surface containing a Mobius band is non-orientable, would be very useful for simplifying the method for determining orientability of surfaces. Colin Rourke, with the aid of a large model, proves the theorem that Mobius bands and any surface which contains a Mobius band are non-orientable. Jeremy Gray begins a look at non-orientable surfaces which cannot be embedded in three dimensional space. Shots of Mobius bands. Using a series of polygonal shapes, Colin Rourke demonstrates the problem of trying to build non-orientable surfaces without boundaries. This leads to a representation, by animated diagram, of a Klein bottle. Jeremy Gray ends the programme with a discussion of why the only surfaces without boundaries which can be embedded in three space, are orientable surfaces.
Master spool number: HOU4005
Production number: FOUM130Y
Videofinder number: 974
Available to public: no