{"id":31049,"date":"2017-05-09T10:02:54","date_gmt":"2017-05-09T14:02:54","guid":{"rendered":"https:\/\/www.shapeways.com\/blog\/?p=31049"},"modified":"2018-02-13T18:49:19","modified_gmt":"2018-02-13T23:49:19","slug":"tutorial-tuesday-16-mathematica-brings-mathematical-bling","status":"publish","type":"post","link":"https:\/\/www.shapeways.com\/blog\/tutorial-tuesday-16-mathematica-brings-mathematical-bling","title":{"rendered":"Tutorial Tuesday 16: Mathematica Brings the Mathematical Bling"},"content":{"rendered":"

Math is the greatest artist. Structure, form, geometry, and symmetry are secret\u00a0keys to beautiful 3D objects. For example, this stunning\u00a0Rhombic star<\/a> by Mathematical Creations:<\/a><\/p>\n

\"3D-printed-rhombic-star-earring\"<\/a><\/p>\n

This design was created with\u00a0Wolfram’s powerful software\u00a0Mathematica<\/a>. The latest\u00a0release of\u00a0Mathematica 11 added a suite of new 3D printing features<\/a>\u00a0including 3D mesh and data utilities, a library of ready-made scientific 3D printable models, and an increased\u00a0ability to thicken and modify Mathematica outputs to make them suitable for 3D printing. In addition, Mathematica can\u00a0send models\u00a0directly to a local 3D printer or a 3D printing service. For example,\u00a0you can use Mathematica to send models to Shapeways right from the command line, like this:<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Printout3D[model, \"Shapeways\"];<\/code><\/p>\n

have a model already? print it now<\/a><\/h4>\n

For this week’s Tutorial Tuesday, we’ll highlight some simple Mathematica commands for creating 3D printable models, then highlight\u00a0three Shapeways designers who use Mathematica in their work.<\/p>\n

From Mathematica Output to 3D\u00a0Model<\/h3>\n

Sometimes Mathematica output is suitable\u00a0for 3D printing, and sometimes it is not. Any number of things could go wrong: The output on the screen could be a 2D render rather than a 3D\u00a0representation that could be exported; or the output\u00a0could be an infinitely thin representation of a mathematical object and therefore not printable; or the output could be exportable, but with a mesh that needs repair.<\/p>\n

Some Mathematica commands that\u00a0can<\/em>\u00a0produce 3D printable output are\u00a0ContourPlot3D<\/a>,\u00a0RevolutionPlot3D<\/a>,\u00a0ParametricPlot3D<\/a>, and Graphics3D<\/a>. With the new Mathematica 11 you can also set thickness using ThickSurface and FilledSurface in\u00a0PlotTheme<\/a>.\u00a0Or control the thickness of your output using Extrusion, PlotStyle, and Tube commands, as shown in these simple examples of thickened, exportable outputs:<\/p>\n

\"Mathematica<\/p>\n

\"Mathematica \"Mathematica \"Mathematica<\/p>\n

print your own design<\/a><\/h4>\n

A 3D Printed Tour of Mathematics<\/h3>\n

One place to find great Mathematica models is Henry Segerman’s Shapeways shop,\u00a0Mathematical Art.<\/a>\u00a0Segerman\u00a0is a math professor at\u00a0Oklahoma State University who uses Rhino, Python, and Mathematica to create astounding mathematical designs.<\/p>\n

\"Screenshot:<\/a><\/p>\n

Want to learn more about the mathematics behind these beautiful 3D prints? Check out Segerman’s new\u00a0book,\u00a0Visualizing Mathematics with 3D Printing<\/a>, where he uses 3D printed models to take a tour through geometry, symmetry, and other mathematical topics. Most of the\u00a0illustrations in the book show\u00a03D printed objects that you can view, download, or order for printing from the book’s\u00a0companion website<\/a>. You can also learn some of the basics of using Mathematica\u00a0for 3D printing\u00a0from \u00a0Segerman’s Notes on 3D Printing<\/a>.<\/p>\n

The Math of the Universe<\/h3>\n

For a wide variety of beautiful designs created with Mathematica, check out the Shapeways shop\u00a0Mathematical Creations<\/a> by Rick Russell:<\/p>\n

\"Screenshot:<\/a><\/p>\n

Make sure in particular to study\u00a0the first model in the screenshot above; it’s a 3D\u00a0projection of a four-dimensional slice of a model of six enfolded\u00a0spacetime dimensions of a ten-dimensional space studied in string theory (!!).<\/p>\n

Math Art and Tutorials<\/h3>\n

Another great Shapeways shop for models created with Mathematica is\u00a0MathArtShop<\/a> by Christopher Hanusa, a mathematics professor\u00a0from Queens College of the City University of New York<\/p>\n

\"Screenshot:<\/a><\/p>\n

Want to learn how to make designs like these? Check out Hanusa’s blog The Mathematical Zorro<\/a>, where he shares wonderfully detailed design walkthroughs of some of his designs, including Mathematica code that you can learn from and modify to make your own designs.<\/p>\n

What do you make with Mathematica? Do you have any tips and tricks to share? Let us know in the comments. We’ll definitely be having another Mathematica post sometime in the future, and we’d love to feature your designs.<\/p>\n

inspired? see your mathematical model in 3D<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"

Math is the greatest artist. Structure, form, geometry, and symmetry are secret\u00a0keys to beautiful 3D objects. For example, this stunning\u00a0Rhombic…<\/p>\n","protected":false},"author":105,"featured_media":31068,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[508,1705,1665,1541,1592],"class_list":["post-31049","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-products-and-design","tag-33-education","tag-math-art","tag-mathematica","tag-mathematical-art","tag-tutorial-tuesday"],"thumbnail":"https:\/\/www.shapeways.com\/blog\/wp-content\/uploads\/2017\/05\/710x528_9690646_6810703_1459356127.jpg","yoast_head":"\nTutorial Tuesday 16: Mathematica Brings the Mathematical Bling - Shapeways Blog<\/title>\n<meta name=\"description\" content=\"Math is the greatest artist. 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