Available online
Description
There are three geometrical problems proposed by the Greeks which have become particularly famous: squaring the circle, trisecting the angle, and duplicating the cube. This last problem is known as... the Delian problem. The programme discusses the reformulation of this problem in terms of finding two mean proportionals (due to Hippocrates of Chios in 450 B.C.) and the solution of the simpler problem of one mean proportional (due to Archytas around 400 B.C.) Finding one mean proportional amounts to finding square roots. The harder problem of two mean proportionals, or cube roots, achieved a new urgency when, according to legend, a plague on the island of Delos was said, by the Oracle, to be removable if Apollo was given an altar of twice the original volume. The Delians consulted Plato, who put mathematicians onto the job. After looking at a mechanical solution implausibly alleged to be Plato's, the programme finishes with one of Menaechmus' truly geometric solutions in terms of conic sections, notably the parabola.
There are three geometrical problems proposed by the Greeks which have become particularly famous: squaring the circle, trisecting the angle, and duplicating the cube. This last problem is known as... the Delian problem. The programme discusses the reformulation of this problem in terms of finding two mean proportionals (due to Hippocrates of Chios in 450 B.C.) and the solution of the simpler problem of one mean proportional (due to Archytas around 400 B.C.) Finding one mean proportional amounts to finding square roots. The harder problem of two mean proportionals, or cube roots, achieved a new urgency when, according to legend, a plague on the island of Delos was said, by the Oracle, to be removable if Apollo was given an altar of twice the original volume. The Delians consulted Plato, who put mathematicians onto the job. After looking at a mechanical solution implausibly alleged to be Plato's, the programme finishes with one of Menaechmus' truly geometric solutions in terms of conic sections, notably the parabola.
| Module code and title: | AM289, History of mathematics |
|---|---|
| Item code: | AM289; 03 |
| First transmission date: | 02-05-1976 |
| Published: | 1976 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:14 |
| + Show more... | |
| Producers: | Jean Nunn; Neil Cleminson |
| Contributors: | Graham Flegg; B. L. van der Waerden |
| Publisher: | BBC Open University |
| Keyword(s): | Delian geometry; Greek mathematics |
| Footage description: | Graham Flegg introduces the programme. He lists the three classical problems of Greek mathematics. Several animations used. B.L. van der Waerden begins his discussion of one of these problems, the Delian problem. He points out that although Greeks and Babylonians could have solved problems of this kind, x3 = a, by numerical approximation, the Greeks preferred to find exact geometrical constructions. Van der Waerden explains, with the aid of animations, how Hippocrates of Chios reformulated the problem in terms of constructing two mean proportionals. Van der Waerden explains why this problem is called the Delian problem. Several still shots of Delos and Greek ruins. Graham Flegg demonstrates a mechanical solution to the Delian problem similar to that given by Archytas. Van der Waerden and Graham Flegg explain how Menarchmus solved the Delian problem by means of conic sections. They use cones and animated diagrams to illustrate their points. Van der Waerden sums up. |
| Master spool number: | AOU1791 |
| Production number: | FOU1936F |
| Videofinder number: | 937 |
| Available to public: | no |
