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The programme deals with the investigations of the parallel postulate of Euclid in the eighteenth and nineteenth century, and concludes with a reference to Einstein's theory of relativity. It is ...presented by Professor Morris Kline of the Courant Institute of Mathematics, New York and Graham Flegg of the Open University. After an introduction setting up the mathematical and historical background, Professor Kline takes up the story in the eighteenth century with Gerolamo Saccheri's attempt to justify Euclid's geometry. He then discusses Gauss' work, and the discovery of a new (hyperbolic) geometry by, in his opinion, Gauss, Lobatchevskii and Bolyai. A model for this geometry is a surface, known as the pseudosphere, in Euclidean Space, A second non-Euclidean geometry is presented: elliptic geometry for which a model is the sphere. The historical and logical significance of the models is discussed, and the programme concludes with a brief look at Riemannian geometries and a reference to Einstein's theory of Space and Time.
Metadata describing this Open University video programme
Module code and title: AM289, History of mathematics
Item code: AM289; 08
First transmission date: 08-08-1976
Published: 1976
Rights Statement:
Restrictions on use:
Duration: 00:24:20
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Producers: Jean Nunn; Neil Cleminson
Contributors: Graham Flegg; Morris Kline
Publisher: BBC Open University
Keyword(s): Euclidean geometry; Geometry; Hyperbolic geometry; Parallel lines
Footage description: Morris Kline makes a brief introductory statement. Graham Flegg introduces the programme by explaining why the inability of mathematicians to prove Euclid's fifth postulate (the parallel postulate) presented problems for Euclidean geometry. Morris Kline and Graham Flegg (voice over animation) examine the contribution, to non-Euclidean geometries, of Saccheri who tried to prove Euclid's fifth postulate in the early 18th century. Morris Kline, with the aid of an animation, points out some of the consequences of following up the 'many parallel line' postulate rather then the 'single parallel line' postulate of Euclid. A new geometry, hyperbolic geometry, results. Morris Kline describes Gauss' contribution to the establishment of hyperbolic geometry. Still of Carl Friedrich Gauss. Graham Flegg examines the contributions of Lobatchevski and Bolyai to the development of non-Euclidean geometries. Stills of Nicholas Lobatchevski, Johann Bolyai and Wolfgang Bolyai. Morris Kline discusses the contribution of Riemann's distinction between unbounded and infinite lines, to non-Euclidean geometry. Animation of a globe is used to illustrate the points. Graham Flegg, using a globe, illustrates some of the theorems of elliptic geometry. Morris Kline, with the aid of animations, discusses the problem of consistency in Euclidean and non-Euclidean geometries. Graham Flegg joins in, then Kline continues. Graham Flegg and Morris Kline discuss the possibility of non-Euclidean geometries modelling real physical space. They look at Riemannian geometries and Einstein's application of them in his theories of relativity as examples. Animations are used to ilustrate points.
Master spool number: 6HT/71818
Production number: 00525_3182
Videofinder number: 943
Available to public: no