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To what extent do the axioms of Euclid apply to different geometries? A form of Euclids axioms is expressed as a set of eight axioms. The set is shown as applicable to plane geometry. However, the ...geometry of the surface of a sphere or the surface of a torus or the non-Euclidean geometry of the Poincare disc each fail to satisfy the complete set of axioms. They satisfy all but the eighth axiom, known in the programme as the similarity axiom. With this in mind the general idea of consistency completeness and independence of axioms in an axiom system is dealt with.
To what extent do the axioms of Euclid apply to different geometries? A form of Euclids axioms is expressed as a set of eight axioms. The set is shown as applicable to plane geometry. However, the ...geometry of the surface of a sphere or the surface of a torus or the non-Euclidean geometry of the Poincare disc each fail to satisfy the complete set of axioms. They satisfy all but the eighth axiom, known in the programme as the similarity axiom. With this in mind the general idea of consistency completeness and independence of axioms in an axiom system is dealt with.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 23 |
| First transmission date: | 1980 |
| Published: | 1980 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:22:55 |
| + Show more... | |
| Producer: | Martin Wright |
| Contributors: | Colin Rourke; Allan I.,1936-2013 Solomon |
| Publisher: | BBC Open University |
| Keyword(s): | Consistent, complete, independent; Euclid; Non-euclidean geometry; Plane Geometry |
| Master spool number: | HOU3255 |
| Production number: | FOUM059B |
| Videofinder number: | 4346 |
| Available to public: | no |
