Mathematics

Day 167 – Umbilic torus

Day 167 – Umbilic torus 640 480 mathgrrl

Today we did not print an umbilic torus.  But we did print a triangular-cross-section mobius strip, which is very close. In yesterday’s post we wished for a way to remesh…

Day 166 – Mobius

Day 166 – Mobius 640 480 mathgrrl

Today I spoke with jamesford007, a student at SUNY Geneseo who is spearheading efforts there to bring 3D printing into the study of mathematics. He shared with me his technique…

Day 162 – Sliced level 3 Menger cube

Day 162 – Sliced level 3 Menger cube 640 480 mathgrrl

We are going to be printing a lot of Menger-type objects, I think. Today’s is a level 3, sliced to reveal the stars. Model again by owens on Thingiverse. Here’s…

Day 161 – Level 3 Menger cube on a filament printer!

Day 161 – Level 3 Menger cube on a filament printer! 640 480 mathgrrl

Thank you, owens at Thingiverse!  You have made the impossible possible.  It was great fun walking this print around the math department today, since everyone there knows just how difficult it…

Day 157 – One-piece Menger cube without internal supports

Day 157 – One-piece Menger cube without internal supports 640 480 mathgrrl

The Holy Grail!  Owens’ model Menger sponge with external support prints a beautiful Level 2 Menger sponge with no internal supports. The difficulty with printing a Menger sponge on a filament-deposition printer…

Day 155 – Menger slice

Day 155 – Menger slice 640 480 mathgrrl

Today we printed owens’ Diagonal Cut Menger Sponge design from Thingiverse. If you sliced a Level 2 Menger sponge in half along a diagonal plane as shown in the picture,…

Day 153 – Stick and lattice trefoil knots

Day 153 – Stick and lattice trefoil knots 640 480 mathgrrl

To finish our collection of trefoil conformations, we have a stick knot and a cubic lattice knot: STL file for stick: http://www.geekhaus.com/makerhome/day153_trefoil_stick_40_25.stl STL file for lattice: http://www.geekhaus.com/makerhome/day153_trefoil_lattice_40_25.stl Thingiverse link: http://www.thingiverse.com/thing:234107 Technical…

Day 152 – Petal and tight trefoil knots

Day 152 – Petal and tight trefoil knots 640 480 mathgrrl

Two more trefoil conformations – as a petal knot (all crossings line up along one center stem) and a tight knot (with the smallest amount of rope length possible given…

Day 151 – Fourier and tritangentless trefoil knots

Day 151 – Fourier and tritangentless trefoil knots 640 480 mathgrrl

Continuing our collection of trefoil knots, today we printed a trefoil in a Fourier-(1,1,2) knot conformation and a trefoil knot in a tritangentless conformation. In other words, the first trefoil…

Day 150 – Trefoil torus knots

Day 150 – Trefoil torus knots 640 480 mathgrrl

For the next four days we’ll be posting various mathematically interesting models of the trefoil knot. Mathematicians consider two knotted forms to be equivalent if one can be transformed into the other…

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