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Slicing a Cone for Art and Science



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Abstract:

2012-09SilverF1.jpgClick to Enlarge ImageAlbrecht Dürer (1471–1528), master painter and printmaker of the German Renaissance, never regarded himself as a mathematician. Yet he used geometry to uncover nature’s hidden formulas for beauty. It was concern for young artists that motivated Dürer to write an ambitious handbook for all species of artists. “The ancients have shown that one can cut a cone in three ways and arrive at three differently shaped sections,” Dürer writes. “… I want to teach you how to draw them.” The curves themselves would accompany a revolution in astronomy. Silver explains that Dürer used geometry to search for beauty, but he never regarded mathematics as a substitute for aesthetic vision. It was a tool to help the artist avoid errors. However, the Painter’s Manual demonstrates that mathematics and, in particular, geometry, meant much more to Dürer. His efforts would influence mathematicians including Cardano and Tartaglia as well as scientists such as Galileo and Kepler.


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