![]() They are very special examples of what are called polyhedra. Introduction: The Convex Regular Polyhedra Also Known as the Platonic Solidsįigure 1 above shows the five Platonic solids. Also, if one moves about, viewing the pieces from different perspectives, various lines and points will suddenly line up, giving quite stunning views try this especially with one eye closed.ġ. The viewer will find it interesting to look at the shadows cast by the pieces. That interaction with the viewer engages one in the choreography of these movements. There is a multitude of dynamic movement both within each sculpture and between the sculptures. The sculptures in this collection do so by calling upon the viewer to inwardly form images and visualize forms in movement, to see in the mind what is suggested by, but is not physically present in, the pieces. In any case, we should not be surprised that we so readily find many connections between mathematics and other arts. Perhaps we should describe Bridges as an organization dedicated to making connections between mathematics and other arts. It is unlike other art forms in that other forms find their expression in physical material. ![]() It is an art form in which the medium is pure thought. The intended audience for the exhibit is anyone who has studied a little high school algebra and geometry, but someone with no mathematical background should find it quite accessible, while those with a sophisticated mathematical background will likely find here some delightful surprises. (The 3D Textbook exhibited at the 2015 Bridges Math-Art conference in Baltimore had actual 3D geometric sculptures, but this website of course can only provide photos of those sculptures.) It is hoped that the exhibit will encourage others to use the Platonic solids as a way to introduce in a very concrete way some abstract mathematical concepts, and perhaps it will also encourage others to create 3D textbooks for other topics in mathematics. The beauty of the sculptures gives a fitting expression to the beauty of the mathematical ideas – a bridge between sculpture and mathematics. So, this “textbook” gives a systematic development of geometric ideas, but does so through a series of more than thirty 3D sculptures with explanatory signs. However, three-dimensional geometry is most effectively presented in three dimensions. A geometry textbook typically develops the ideas with text and two-dimensional drawings. The richness of ideas found in the Platonic solids gives a wonderful example of the beauty to be found in mathematical thought.
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