Wednesday, May 18, 2011

Triangulation Error


Oh Lord!!! Does it mean he was not perfect? An article by by Dirk Huylebrouk in the March 29, 2011 issue of Scientific American, Lost in Triangulation: Leonardo da Vinci's Mathematical Slip-Up, claims that a geometric drawing by da Vinci contains an error, according to Dutch mathematician and sculptor Rinus Roelofs.

Helical Holes by Rinus Roelofs.- Based on Isosidodecahedron.
This is a "rapid prototype" printed in a 3D printer based on a computer model.

The rhombicuboctahedron as it is called, (I'm sure you remember it from your geometry class:-) is one of the many geometric figures that Leonardo illustrated for his teacher and collaborator Luca Pacioli. The figure Rinus refers to is the "intelligent rhombicuboctahedron", as Leonardo used to call geometric figures whose sides or facets had been "elevated" to a common vertex.

The "intelligent" version Rinus refers to.


The figures appear in Pacioli's book De Divina Proportione, an extraordinary book on the principles of design that any artist should study.

Painting of Luca Paccioli, attributed to Jacopo de' Barbari, 1495. Table is filled with geometrical tools: slate, chalk, compass, a dodecahedron model. A rhombicuboctahedron half-filled with water is suspended from the ceiling. Paccioli is demonstrating a theorem by Euclid. (Source:Wikipedia)

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