For those interested in exploring how desktop 3D printers can delve deeper into math and geometry than early grade math manipulatives, check out the work of George W. Hart, mathematical sculptor/designer, who with each new development in rapid prototyping technology continues to lead the way to create remarkable models and sculptures in the 3D printing space. (He created separate pages for the work he printed at home with each of his first three desktop 3D printers: the MakerBot CupCake CNC, Thing-O-Matic, and Replicator.)
As Hart is as passionate a mathematician as an artist, time spent exploring his site, papers, and talks is well worth the effort to learn more about the various phenomena that create such fascinating forms. And while his work has appeared in museums and exhibitions world over, he has also gained a bit of welcome Internet prestige as the father of the delightful mathematical filmmaker/illustrator Vi Hart.
Rapid Prototyping or Solid Freeform Fabrication refers to a range of new technologies which construct physical three-dimensional objects by assembling thin layers of material under computer control. Objects can be made which are extremely accurate, complex, and beautiful, and which no other technology can produce….
Presently this is a somewhat expensive technology used mainly in high-end product design, and in research universities. But in the future, the cost will certainly come down and everyone will be able to create amazing physical objects with these machines. Consider how laser printers cost hundreds of thousands of dollars in the 1970’s but now are commonplace in every school and business; I similarly expect rapid prototyping machines to be ubiquitous and inexpensive in ten years, available in all universities, at most high schools, at the copy shop down the street, etc. There will be many applications to art, mathematics, and education which I am beginning to explore now.
As a sculptor I am necessarily interested in three-dimensional geometry. As a hobby I am also interested in the mathematics of four-dimensional geometry. From a 4D object, one can calculate 3D “shadows” which are often beautiful but very complex objects. RP machines can easily produce these structures, which are stunning to look at even if one doesn’t understand the underlying higher-dimensional ideas behind them….