Available onlineViewing permission denied
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.
