This fall I’ll be a Research Fellow at the Institute for Computational and Experimental Research Mathematics (ICERM), for the Illustrating Mathematics semester program. The goal of the program is to “bring together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools.” Over 100 mathematicians and artists will come together at ICERM for a series of conferences, workshops, exhibits, and even semester-long research collaborations.
The exhibits include art exhibits and displays at ICERM, Brown, RISD, and the AMS Headquarters. The call for art submissions just wrapped up and we submitted five things. The first is a series of stainless steel knots that we discussed in our earlier Hacktastic post Knots in OpenSCAD with Sweeper. Here’s our submission:
The math part
Knots are embeddings of circles in 3-dimensional space, but they are typically studied in terms of their projections into 2-dimensional space. We can use 3D printed models to investigate knots in a more 3-dimensional way. This series includes nine Stainless Steel 3D printed knot conformations: Tritangentless Trefoil, Figure Eight Stick Knot, Cinquefoil Lattice, 5_2 Lissajous, 6_2 Petal Knot, two (7,2) Torus Knots, 8_19 Hyperboloid Stick Knot, and Midway Perko Knot.
You can read about each of these knots, and even download free files and order your own 3D printed copies, at these links:
- Tritangentless Trefoil Knot — read more at MakerHome, Day 268
- Figure-Eight Stick Knot — read more at MakerHome, Day 269
- Cinqefoil Lattice Knot — read more at MakerHome, Day 272
- Lissajous Three-Twist Knot — read more at MakerHome, Day 273
- Miller Petal Knot — read more at MakerHome, Day 276
- Torus Knot (7,2) and equivalent Torus Knot (2,7) — read more at MakerHome, Day 286
- Hyperbolid Stick Knot — read more at MakerHome, Day 67
- Midway Perko Knot — read more at Hacktastic, Giant Spiky Perko Knot
The printing part
The knots were scaled before construction to form a consistent series while preserving thickness. This is one of the great advantages of using parametric modeling software like OpenSCAD to create these models; we can determine the overall size of the model first, adjust our functions and data accordingly, and then sweep out the path of the knot with the same thickness of every other knot in the collection. For more information, see our Hacktastic post Knots in OpenSCAD with Sweeper and the Math sculptures with sweeper files we put on Thingiverse.
Each of the nine knots were 3D printed at Shapeways in Stainless Steel. Our original Special Knot Collection actually includes one more knot, a link of three circles called the Borromean Rings. The Borromean Rings could not be included in our Steel collection because Shapeways does not currently offer 3D printing of interlocked objects in Stainless Steel. You can find all nine of the knots in our Steel series in the Steel Knot Collection in our Shapeways shop.
Check them out in action (be sure to watch to the end!):
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