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In the first part of this programme it is proved that a section of a cone is an ellipse. In the second part the different conic-sections, obtained when a plane is rotated through a cone, are discussed.
Metadata describing this Open University video programme
Module code and title: M101, Mathematics: a foundation course
Item code: M101; 18
First transmission date: 09-07-1978
Published: 1978
Rights Statement:
Restrictions on use:
Duration: 00:24:30
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Producer: Jack Koumi
Contributors: Norman Gowar; John Mason
Publisher: BBC Open University
Keyword(s): Ellipse; Directrix; Focus; Parabola; Hyperbola; Conics
Footage description: John Mason introduces the programme and looks at the geometric properties of an ellipse. He then moves on to examine an ellipse as created by a cone sliced by a plane. Norman Gowar proves that this is an ellipse by using two spheres which touch both the cone and the plane. The two focus points of the ellipse occur where the spheres contact the plane John Mason now examines what happens as the plane is moved through the cone, and as the cone is moved across the plane. The latter is demonstrated by shining a torch at different angles. With the aid of computer animations John and Norman examine the resulting sectional shapes as the plane is tilted through the cone. They obtain a parabola, a circle and a hyperbola. By tilting from the horizontal through to the vertical they cover all possible cases. These positions are shown again on the computer. John Mason then redefines the conies to fully integrate the parabola into the sequence. Norman Gowar demonstrates how this description is arrived at. All the conics are described in terms of their eccentricity, the distance to the focus divided by the distance to the directrix.
Master spool number: 6HT/72532
Production number: 00525_4256
Videofinder number: 2474
Available to public: no