Available online
Description
The programme deals with the origins of co-ordinate geometry in the early seventeenth century (seen in the bringing together of algebra and geometry). It is presented by Professor Boyer of Brooklyn... College, New York and Graham Flegg of the Open University. Although the Greeks, and much later Nicole Oresme in France, had had some inkling of co-ordinate geometry, the subject really begins with the application by Descartes of the new methods of algebra to a classical problem of Pappus: the locus to three or four lines. Descartes was led to an algebraic classification of curves and a programme for the geometric solution of algebraic problems. Independently, Fermat analysed conic sections algebraically. Both established the key idea that two unknowns related by one equation define a locus. The programme concludes with the first thorough introduction of modern (positive and negative) co-ordinates by Newton in his classification of cubic curves.
The programme deals with the origins of co-ordinate geometry in the early seventeenth century (seen in the bringing together of algebra and geometry). It is presented by Professor Boyer of Brooklyn... College, New York and Graham Flegg of the Open University. Although the Greeks, and much later Nicole Oresme in France, had had some inkling of co-ordinate geometry, the subject really begins with the application by Descartes of the new methods of algebra to a classical problem of Pappus: the locus to three or four lines. Descartes was led to an algebraic classification of curves and a programme for the geometric solution of algebraic problems. Independently, Fermat analysed conic sections algebraically. Both established the key idea that two unknowns related by one equation define a locus. The programme concludes with the first thorough introduction of modern (positive and negative) co-ordinates by Newton in his classification of cubic curves.
| Module code and title: | AM289, History of mathematics |
|---|---|
| Item code: | AM289; 06 |
| First transmission date: | 13-06-1976 |
| Published: | 1976 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:25:00 |
| + Show more... | |
| Producers: | Jean Nunn; Neil Cleminson |
| Contributors: | Carl Boyer; Graham Flegg |
| Publisher: | BBC Open University |
| Keyword(s): | Algebra; Analytic geometry; Co ordinate geometry; Descartes; Fermat; Oresme |
| Footage description: | Graham Flegg introduces the programme. Still of Manhattan and an animated map are used to convey the principles of coordinate geometry. Graham Flegg describes some of the Locus problems solved by the ancient Greeks. Animations illustrate his points. Carl Boyer discusses Pappus' work with loci problems particularly his classification of the three curves known in antiquity. Boyer goes on to describe an early attempt at a coordinate geometry by Oresme. Animations are used to illustrate the points. Graham Flegg joins in. More animations. Flegg and Boyer briefly point out the bar which lack of a good symbolic notation imposed on further development of analytic geometry. Boyer goes on to discuss Descartes' contribution to coordinate geometry. Animations and graphics illustrate points made. Graham Flegg joins in. More animations. Boyer examines Fermat's contribution to coordinate geometry, particularly his work on loci. Graham Flegg joins in. Several animations are shown. Boyer sums up. |
| Master spool number: | 6HT/71816 |
| Production number: | 00525_3180 |
| Videofinder number: | 940 |
| Available to public: | no |
