Geometry and the Liberal Arts by Daniel Pedoe

By Daniel Pedoe

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In Figure 20, which shows a rectangle AEFD in golden sectIOn constructed from a square ABCD, continue the construction by draw. a square BEF'C' , and show that EFis also divided in golden sec109 tion at F'. Can you continue? -6 LEONARDO DA VINCI ·3 · LEONARDO DA VINCI LEONARDO DA VINCI (1452-1519) is one of history's enigmas. He has been hailed as a consummate artist, a genius of the first water, a great scientist who anticipated many inventions which were not realized until the twentieth century, and so on.

If from any point P on the ellipse we drop a perpendicular PM onto the line n = AA', this line extended will meet the surface of the cone again in a point Q, where PM = M Q. But the line PM Q lies in the plane of the ellipse, and therefore Q is a GEOMETRY AND THE LIBERAL ARTS ALBRECHT DORER point on the ellipse such that PM = M Q. The line n is therefore an axis of symmetry of the ellipse. We have been talking about correct perspective. The eighteenthcentury painter and engraver William Hogarth produced an amusing print labelled False Perspective (Plate 16) in which many absurdities are apparent.

Leonardo was an immensely practical artist, and not at all disposed to adhere rigidly to a theory if the resulting picture made the viewer uncomfortable. Of course, the possibilities of adjustment in the human eye are very great, so much so that people become rather disturbed if this is pointed out to them. We have all watched the full moon rising above the horizon. It looks enormous, but when it is at its highest point in the night sky, it looks much smaller. Years ago I was having a meal in a guesthouse* with about a dozen people, of all professions, when this subject came up.

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