Mathematics and art II: Albrecht Dürer

Abstract

A l b r e c h t D i i r e r (1471-1528) trave led to Italy as a young man to learn the secre ts of perspect ive , probably f rom Luca Pacioli. A mathemat i cian with much original work to his credi t including new curves, perspect ive machines , the nets wi th which to bui ld po lyhedra and some new polyhedra, Dtirer also wrote for the pract i t ioner on how to use ma themat ics in cons t ruc t ion and design. These b o o k s were copied widely over 300 years and inspired much la te r mathemat ics . In St. Jerome in his Cell (1513-14), one of the three mos t famous of Dtirer 's engravings, we see an example of exac t geometr ic pe r spec tive wi th an approach which is dist inct ly different from that used in Italy. The ex t reme shor tness of the perspective d is tance indicates that the room would be at mos t four feet long if actually const ructed . The vanishing poin t is t/4-inch f rom the right edge, and as a consequence of this p l acemen t the p ic ture s eems cosy and uncramped . Each objec t is p laced with pe rspec t ive in mind, and so is or thogonal to the picture, para l le l to it, or at a 45 ~ angle. Note the s l ippers on the l e f t o n e is paral lel to the wall and the o ther is perpendicu lar to it. The celebrated, studied, and of ten copied engraving, Melancolia I, on a miniature shee t f rom Aitutaki, contains more than two dozen objects for us to interpret . Poss ib ly the concern of the dark androgynous winged figure is the quadra ture of the circle: note the sphere, compass , and po lyhedron which is t runca ted so we can see four faces. Agr ippa ' s 4 • 4 magic square (which Dtirer p robab ly learned of f rom Pacioli) is affLxed to the a lchemists ' tower behind the figure. The date of the engraving, 1514, appea r s in the bottom line of the magic square.