Day 303 - Hello Octopus: A simple first print for the Mini

This is the second in a series of posts about getting started with 3D printing, and the printer we'll be using along this journey is the MakerBot Replicator Mini. If you have a different sort of printer I hope you can still get something out of these posts, although admittedly they are going to include a lot of Mini-specific walk-thoughs and technical hardware and software discussions, at least at first.

The first thing I recommend printing on the Mini is Cute Octopus Says Hello, one of MakerBot's own designs on Thingiverse and the model they use for illustrating their filament colors. This is one of the simplest designs you could choose: it has no overhangs, nothing complicated, and it scales well. In fact we're going to print a mini-version at 50% scale.

Thingiverse link: http://www.thingiverse.com/thing:27053

Our octopus-printing is going to be split over three days. Today is Level 1: Straight up easy. We'll print the octopus shown on the left in the picture above, with no special modifications or settings. Tomorrow and the next day we will level-up to changing some settings that speed up the print and use less filament.

Step 1: Load the model. 
From the MakerBot Desktop software, click "Explore" and then search Thingiverse for "cute octopus says hello". The model we'll be using should be first in the list, and dated June 31, 2012. Click on the model and then click the red "Prepare" button to see the file. Then click the new "Prepare" button near that file to load it into the software.

Step 2: Rotate the model.
This isn't necessary but it seems kind of unfriendly for the octopus to face away from us, so we'll turn it around. Click on the octopus and then click on the "Turn" button. The bottom of the three options will rotate the model around the vertical z-axis. Click the third "+90" button two times to turn the octopus around.

Step 3: Scale the model.
Since we're on a Mini we'll start by printing "mini" at 50% scale. Of course this will also make the print a lot faster; this is a linear decrease to 50% scale, so the volume will decrease by much more (we'll talk more about this later). Click on the "Scale" button, type in 50.00% percent in the "Scale To" box, and press Return/Enter.

Step 4: There is no step 4. 
This is the easy day, remember? Let's color inside the lines for this first print, and not change anything under the "Settings" tab.

Step 5: Press Print!
Okay now you can press the red "Print" button. This will bring up a window that shows how much time and filament the print will cost you. Before printing click "Print Preview" so you can check out what the Mini will be doing as it prints.

Step 6: Print Preview.

For a simple print like this one, we don't actually need to look at the Preview; it's just interesting. Move the vertical slider on the left of the window to see what the printer will do at various levels. This is perhaps clearest if you first click "View from Top" and then move the slider. At each level of the print the nozzle will follow the path shown at that level. The screenshot below shows a level around halfway up; you can see the eye indentations at this level. You can also see the vaguely hexagonal filler material in the center of the model. The slicing software uses this filler for any interior solid parts of your model, to save filament and time. The default settings are for the interior fill to take up 10% of the space, with the other 90% as empty space. We'll mess with the default settings later, but not today.

When you're done looking at the Preview just click "Close" and then select "Start Print" to start your print. Or you could just stare at the printer for five minutes wondering why nothing is happening and then realize that even though you hit "Print" earlier you still have to hit "Start Print" now. That's how I did it and things turned out okay in the end.

Step 7. Wait and watch and other stuff and then remove your print.

After about 40 minutes (give or take 5-10 minutes and plus a five-minute warm-up), your print should be ready. Remove the build platform from the machine and then remove the model from the platform. 

Step 8. Remove the raft. 

There will be a "raft" at the bottom of the model that you need to pull away. You may find it useful to use some sort of pliers or tool. Two pieces of advice: First, try to tear off the raft instead of cutting it away. It works best if you can manage to get it off all in one piece, just like when you try to remove a price label from the bottom of a plate or a glass; otherwise you'll have to spend time removing the little bits that got left behind. Second, be reasonably careful. It is possible to get poked by the PLA and in fact that happened to me today because I figured hey I'll just yank this off carelessly, what could happen I've printed like three of these octopuses already so this PLA can't hurt me I am invincible. Then I had to pull a PLA splinter out of my thumb. Here's a picture of what the raft looks like, alongside the finished model:

Next time: Advanced settings!

Day 302 - Setting up the Mini

Today my 9-year-old assistant Calvin will be setting up a Replicator Mini. This is the start of a series of posts on how to get started with a 3D printer, what you might try printing first, how to modify existing designs and make your own, what supplies you might want to have on hand, and things you can do in the classroom or with your own kids.

The Mini was built to be easy, and as far as setup is concerned it definitely is, as Calvin will now demonstrate. The extruder snaps into place with a strong magnet:

Then you put the filament spool in the back, pull the filament through the tube, and seat the tube clip near the spool. Make sure your spool has the filament feeding from below into the clip:

Then insert the end of the filament into the top of the extruder:

Finally, snap in the build plate:

Once the printer is set up you have to install the MakerBot Desktop software. For those of you with pre-5th-gen machines, Desktop is different from MakerWare, and it's both more and less powerful at the same time: it's more powerful in the sense that it is connected to Thingiverse and a Library of your designs, but less powerful in the sense that there is a lot less flexibility with custom profiles and settings. The same is true of the machine itself: it's more powerful, has a better extruder, etc, but it's not made to be taken apart and repaired like the trusty Replicator 2 was.

Once you get Desktop installed, it is a good idea to immediately update your firmware. From the menu at the very top of the MakerBot Desktop screen choose Devices/Update Firmware, then download the firmware. The process takes a while and then the printer will restart. If you have a problem with your prints, the very first thing that Support is going to ask is whether or not you have updated your software and firmware, so you might as well do it now!

Here are some links to help you finish setting up and get started on your first print:

• MakerBot Getting Started pamphlet for the Mini
• MakerBot Mini Reference Guide
• MakerBot assembly video of the entire setup process
• Download site for the MakerBot Desktop software
• MakerBot Printshop app for creating a few easy prints from your iPad

To get started right away you can try one of the example files that come with the Mini: From the menu at the very top of your screen while in the Desktop software, look under File/Examples for various things that you can print.  In tomorrow's post we'll have another recommended "first print" you can try. 

First impressions so far: The Mini is built to help you learn fast, but it forces you to color inside the lines. This is great for getting started, but when you want to tinker outside of the lines it can be a challenge. Nothing we can't fix, though! Over the next few weeks we'll explore both how to print things quick-and-easy and how to break the rules and go further to tinker and modify prints on the Mini.

Days 301+ to be posted in BROOKLYN!

This blog is officially on hiatus until after we finish moving to Brooklyn. Stay tuned for the end of next week when we'll post the exciting news from this week about our new printer and how it works!

See you on the other side, good old MakerBot Replicator 2...

Day 300 - Divisibility by 100 celebration with 400 Menger sponges!

We are at Day 300 in our year-long print-a-day project, thank goodness. In celebration, today's print is a HUGE LEVEL 4 MENGER SPONGE, built out of 400 tiny Level 2 Menger sponges printed with a bunch of Replicator 2 and Afinia H-Series machines at home and at work over the last few weeks.

This model is now disassembled and the 400 tiny cubes will be given away to those who attend my Math Encounters talk at MoMath in NYC next week. The talk is free but you have to register in advance at one of the links below:

Making Mathematics Real: Knot Theory, Experimental Mathematics, and 3D Printing

• Wednesday, July 2 at 4:00 PM
• Wednesday, July 2 at 6:30 PM

Here is a close-up picture of the Level 4 assembly:

Thingiverse link: http://www.thingiverse.com/thing:372888

Settings: These cubes were printed using owens' clever external-support-stand method, with no support needed. We used Replicator 2 machines with raft but no supports, and Afinia H-Series machines with as little support as the software allows on a Mac. 

Technical notes, assembly flavor: Because of the overhangs in the Level 4 Menger sponge, we had to use a few pieces of paper in the assembly so that things would stay in place without using glue. You can see the papers we used in the time-lapse sequence below. (Shout-out to dayofthenewdan's great Time Lapse Assembler software, which made it very easy to piece our sequence of pictures into a short video.)

Here is another time-lapse sequence, this time from the side:

Day 299 - Tricolored representation of 7_7

Today we are finally at the end of the 15-knot series of knot conformations that we started on Day 266. This one is a tour-de-force, made by printing out separate pieces and heat-gluing them together afterwards! It is a tri-coloration of the the last seven-crossing knot, 7_7. 

Thingiverse link: http://www.thingiverse.com/make:82553

Settings: MakerBot Replicator 2 + heat gun!

Technical notes, math flavor: Knot colorings are one of the simplest examples of invariants, and a good place to start if you are interested in knot theory. A proper 3-coloring of a knot projection is a coloring of the strands of the knot with three colors so that at each crossing, either all three strands coming into the crossing are the same or all three strands coming into the crossing are different. If you're interested in learning more, here are two papers I wrote with students about knot colorability:

• p-Coloring classes of torus knots, with Anna-Lisa Breiland and Layla Oesper
• Counting m-coloring classes of knots and links, with Kathryn Brownell and Kaitlyn O'Neil

Technical notes, design flavor: This knot was made by JMU student Jonathan Gerhard using TopMod. Here is what he has to say about his design process for this knot model:

This knot started with the typical model for 7_7, exported from KnotPlot and then imported into TopMod. Note that in TopMod, holding down option and then clicking will allow you to rotate the view. Start by going to Selection/Select Edge Ring so that your selection tool will select rings around the model with each click. 

Then click on the mesh where you want to separate the pieces. For example, to isolate the strand I labeled "4" in the files, I made the selections pictured below and then went to Edit/Delete Selected. 

After deleting the sections it looks like this:

Now highlight the rest of the knot by pressing Shift while highlighting the edges of the mesh. For example, here's a fully highlighted knot that I got while trying to isolate strand "6":

Again, choosing Edit/Delete Selected allowed me to isolate the strand, after which I could Export it from the file menu as an STL. 

Finally, click the yellow back/undo arrow to get back to the entire knot, choose a ring of mesh one edge over so that the next strand includes the bit you originally cut away, and cut away the strand you already made. Here's the whole knot after segment "4" is exported and cut out: 

Repeating thie process with each strand allows you to isolate each piece and print them off in their respective colors. Then you can glue them together after printing. 

Here is a picture of the five JMU students in the 3-SPACE Math 297 class that constructed the knots in this series. From left to right are Patrick, Jonathan, Kirill, Greg, and Taylor. This picture was taken right after their double presentation and 3D-printing demo at the MD/DC/VA MAA meeting this spring. (And yes, two of them showed up to the presentation wearing Ecogeeco's 3D Bow Tie from Thingiverse!)

Day 298 - Friday Fail: Down but not out - also come see me July 2 in NYC!

Still trying to pack up 14 years of house and move it to a Brooklyn apartment, and that is taking pretty much all my time these days. Since I seem to be a failure expert I will try to practice the number one rule about failure: that it is a temporary condition. I will get back to the blog soon, and fill in the missing posts before this one.

In the meantime, if you live in the NYC area, you might be interested in my Math Encounters talk about mathematical 3D printing at MoMath, the Museum of Mathematics, on July 2. That's just one day after we move so I'll probably be very well-rested and give an excellent talk, right?

If you come to the talk please introduce yourself to me afterwards; I'd love to meet people from the area who are interested in 3D printing. Here are the links to register for the event; it's free but you have to register before it fills up:

“Making Mathematics Real: Knot Theory, Experimental Mathematics, and 3D Printing” July 2 at 4:00 PM

“Making Mathematics Real: Knot Theory, Experimental Mathematics, and 3D Printing” July 2 at 6:30 PM

Notice the giant 10_125 knot from Day 11 featured on the poster! And that Jennifer Lawton, President of MakerBot, will also be speaking!

Also yes, I did print something today: A tiny version of vertox's beautifully curved Shy-light. I don't intend to put a light in this one; I just wanted to be able to see and feel the shape so I could understand it a little better. Here is the view from underneath:

Thingiverse link: http://www.thingiverse.com/make:82143

Settings: Printed on a MakerBot Replicator 2 with translucent filament at 30% scale, on .3mm/low with a raft, on blue painter's tape on a glass build plate, in just 14 minutes.

Day 297 - Borromean rings for the fourth dimension

Today we reprinted a giant red model of the Borromean rings from our Borromean Rings Collection on Thingiverse that we made on Day 178, to replace the giant blue model pictured there. The blue model is now on a trip to the UK to Matt Parker (standupmaths on Twitter), who will be photographing it for a chapter in his upcoming book Things to Make and Do in the Fourth Dimension. We will miss you, blue rings. Long live red rings!

Thingiverse link: http://www.thingiverse.com/make:82550

Settings: This model prints as one piece with almost no support at all. Here it is just after printing on our REPLICATOR 2 WE STILL LOVE YOU PLEASE DO NOT BE DISCONTINUED.

Day 296 - Spiral conformation of 7_6

The penultimate knot in our series is the knot 7_6, in both standard conformation and the spiral S(5,2,(1,1,-1,1)) conformation from Day 234.

Thingiverse link: http://www.thingiverse.com/make:82547

Settings: Makerbot Replicator 2 on .3mm/low with custom knot slicing settings. The knot requires almost no support material if you print it end-up instead of flat on its side.

Technical notes, spiral flavor: It isn't known whether or not all knots have a spiral representation. As of the time of this blog post we know that eight of the fifteen knots through seven crossings are spiral. The spiral notation S(n,k,(....)) denotes that the knot can be represented as an n-strand braid periodic knot with k repetitions and over/under spiral pattern determined by the vector in parentheses.

• 3_1 is a torus knot so has two spiral representations: S(2,3,(1)) and S(3,2,(1,1))
• 4_1 has spiral representation S(3,2,(1,1))
• 5_1 is a torus knot so has two spiral representations: S(2,5,(1)) and S(5,2,(1,1,1,1))
• 6_2 has spiral representation S(5,2,(1,1,1,-1))
• 6_3 has spiral representation S(5,2,(1,1,-1,-1))
• 7_1 is a torus knot so has two spiral representations: S(2,7,(1)) and S(7,2,(1,1,1,1,1,1))
• 7_6 has spiral representation S(5,2,(1,1,-1,1))
• 7_7 has spiral representation S(5,2,(1,-1,-1,1))

Day 295 - Tangle conformation of 7_5

Just three knots left in the conformation series that we started on Day 266! Today we have the knot 7_5 in a tangle conformation, where you can clearly see the Conway notation [322] for this knot; note the one three-twist and two two-twists in the red model on the right:

Thingiverse link: http://www.thingiverse.com/make:82546

Settings: MakerBot Replicator 2 with our usual custom knot slicer settings.

Technical notes, KnotPlot flavor: This knot was made by JMU student Greg Houchins using KnotPlot. Here is what he has to say about his design process:

A particularly visual way to make a printable tangle-based knot  is with KnotPlot's Rational Tangle Applet that gives you one rational tangle to twist on the top, bottom, left, or right in any direction.  This provides a way to visualize the physical construction of the knot but is limited by its inability to follow Conway notation directly.  To make specific knots given their Conway notation, it is easier to use KnotPlot's Rational Tangle Calculator. This calculator includes the ability to make, transform and adjoin all the tangles need to follow the usual tangle construction algorithm. 

To make the 7_5 model (with Conway notation [322]), open the KnotPlot Tangle Calculator and click on the number 3 to create the tangle with 3 clockwise rations.  Then transform the knot with the r button and press the number 2 button to form the tangle with two clockwise rotations.  To adjoin them, press the # button. Then transform them again with the r button, make another tangle with 2 rotations, and adjoin them with #. To finalize the knot, press the N button to make the numerator knot, which is what we want.  One this knot is formed, we can export it as an .obj file by going to the KnotPlot command line and typing objout 7_5knot (where "7_5knot" is the title of the file it will create).

Day 294 - Secret push-pin shelf

One more push-pin print; this time we took another design by Tosh on Thingiverse, his Secret Shelf, and scaled it down for use on the corkboard. Our first attempt was a reduction to 60% scale, shown on the left in orange; this is the bottom of the shelf but we are using it upside-down since it was too small to have a proper lid (it would have crashed into the push-pins). The second attempt is shown on the right with a dollar hiding inside, at 80% scale.

Thingiverse link: http://www.thingiverse.com/make:82541

Settings: Printed on a Replicator 2 with .3mm/low layer resolution and at 60% and 80% scales.

Day 293 - Push-pin push-pin-less holder

Today we printed a push-pin-less push-pin, for those times that you don't want to leave a hole in your object; the design is Tosh's beautifully simple Wall mount paper clip from Thingiverse.

Thingiverse link: http://www.thingiverse.com/make:82539

Settings: Replicator 2 on .3mm/low, printed with the object on its side so that supports are not needed. The push-pin hole came out well even in that orientation.

Technical notes, Father's Day edition: Happy Father's Day everyone! To celebrate we took Phil out to a mountain cabin for some analog relaxation time. Sort of the opposite of what we'll experience when we move to NYC next week. Here is what it looked and sounded like at dawn, with the sun just coming up over the beautiful Shenandoah Valley mountains:

Day 292 - Push-pin push-pin holder

Today is Saturday and we are printing things for young C, who needs things for his corkboard. First, a push-pin holder that is held up by push-pins, JamieLaing's Thumbtack-able Thumbtack Holder from Thingiverse:

Thingiverse link: http://www.thingiverse.com/make:82538

Settings: The usual .3mm/low layer height with a Replicator 2. The thumbtack holes came out just the right size and the model is quite sturdy.

Day 291 - Friday Fail: Crossing change edition, with Pretzel conformation of 7_4

The most eagle-eyed of you may have noticed an error in one of the knots in the group photo of the knot conformations series on Day 266. We got one of the crossings wrong in 7_4!

Specifically, we accidentally made a print of P(-3,1,-3) - that is, three negative twists on the left, one positive twist in the center, and three negative twists on the right - when we needed a print of P(-3,-1,-3). Since we reversed the crossing in the middle we made a knot that can be moved into a projection with fewer than seven crossings. If the knot were made of rubber, we could grab the overstrand of the center crossing and stretch it out around the outside of the knot, eliminating three crossings. This means that the knot we printed has a crossing number of at most four, so must either be 4_1, 3_1, or the unknot. Bonus question: Can you tell which?

Here is the fixed version, although to confuse you we decided to swap all of the *other* crossings instead of changing the center one. In other words, we printed the pretzel knot P(3,1,3), which is still a conformation of the knot 7_4.

Thingiverse link: http://www.thingiverse.com/make:82536

Settings: MakerWare .3mm/low on a Replicator 2 with custom knot slicing profile.

Technical notes, math flavor: This knot was made by JMU students Greg Houchins and Kirill Korsak, who used Mathematica's KnotData package to export an STL file of this pretzel conformation. How did they know this pretzel knot is 7_4? Because they computed its knot determinant and the answer was 15. Since the pretzel knot above is in a projection with 7 crossings, we know that its crossing number is at most 7, and therefore that it is one of the first fifteen knots in the Rolfsen table. Only one of those knots has determinant 15, and that is 7_4. Below is a handy table of determinants for the knots through 7 crossings, generated by the amazing KnotInfo site.

Day 290 - Cantarella conformation of 7_3

Today's knot conformation takes us back to the beginning of my 3D-printing journey in February 2013, when I got my first 3D printer - still my favorite - a MakerBot Replicator 2. (Sad note: I think this fantastic printer has been discontinued, as it is consistently out of stock on the MakerBot site. Too bad, because this is the best 3D printer I have ever had the pleasure of using. I have one at home, one in the JMU MakerLab, two in the JMU 3-SPACE Classroom, and I wanted to get some of them for MoMath when I start there this fall.)

Back in early 2013 my entire motivation for getting a 3D printer was to print knots, since that is what I usually study when I am wearing my math professor hat. Specifically, I wanted to print knots in a minimum conformation, that is, knots that were as tight as possible. Of course it is difficult to see what tight knots are doing since they are all bunched up, so many of my early prints of tight knots were "blown out" - really meaning that the strands were made thinner - so that there would be space between the strands; for example see Day 9 and Day 11. Today's conformation of 7_3 is a true "tight" conformation, pulled together as closely as possible. The data for this knot was kindly provided by Jason Cantarella from the Department of Mathematics at the University of Georgia, also known as DesignByNumbers on Thingiverse, where he has provided files for a very large number of minimum-conformation knots and links.

Thingiverse link: http://www.thingiverse.com/make:82272

Settings: Printed on a MAKERBOT REPLICATOR 2 I LOVE YOU PLEASE DO NOT BE DISCONTINUED.

Day 289 - Braid representation of 7_2

Continuing with the knot conformations series we started on Day 266, today we printed a braid representation of the knot 7_2.

Thingiverse link: http://www.thingiverse.com/make:82269

Settings: Printed on a Replicator 2 with our custom knot support profile.

Technical notes, Mathematica/Blender/Tinkercad flavor: This knot was printed by JMU student Patrick Moran, using Mathematica to get the original braid shape, Blender to thicken the strands, and Tinkercad to add bars at the top and bottom of the model. Here is what he has to say about his process:

For the knot 7_6 I decided to show a simple braid representation, where the crossings occur between adjacent strands in a series of strands that we imagine as connecting up at the ends (that is, the first strand at the top bar is connected to the first strand on the bottom bar, and so on). Every knot has such a braid representation; see Colin Adams' Knot Book for a nice proof of this. To get a 3D model of the braid representation I used Mathematica, with commands as shown in this screenshot:


After exporting we used the Blender-thickening method from Day 285 to thicken the strands, and added bars to the top and bottom using Tinkercad.

Day 288 - Micron Bach

One of the things I had to give up to move from a house in the country to an apartment in Brooklyn was my drum set. Apparently you have neighbors and stuff when you live in an apartment building, and not all of them appreciate loud banging noises. In the hopes that I'll find time to turn my musical attentions to learning how to use our Alesis Micron synthesizer, today I printed a little Bach bust to sit on the Micron, from ad1124's very nice bach_final Digitizer-scanned model on Thingiverse:

Thingiverse link: http://www.thingiverse.com/make:82268

Settings: Printed on a MakerBot Replicator 2 with MakerWare .2mm/standard; that's better resolution than I usually use, but I wanted to make sure to capture the details of the model.

Day 287 - Grocery bag holders

In preparation for walking groceries home from the shop in the big city, today we printed three of ivanseidel's Bag Holder model on Thingiverse (one for each of us in the family). There are a number of bag holders on Thingiverse but the design of this one is particularly sturdy and elegant, with large comfortable handles. I think they look like elephants somehow. Try making one and having people guess what it is. So far none of the people I have asked have been able to figure it out on their own, although they come up with a lot of strange and interesting guesses!

Thingiverse link: http://www.thingiverse.com/make:82266

Settings: MakerWare .3mm/low with no raft and no supports. The print is quick and light despite looking rather large.

Day 286 - Torus conformations of 7_1

Today we have two torus knot conformations of 7_1. A torus knot is one that can be drawn on the surface of torus ("inner tube" shape) without intersecting itself. A T(p,q) torus knot wraps around the torus like a clock p times, and around the handle of the torus q times. The standard conformation of 7_1 in the knot table is shown on the left, in the form of a T(2,7) torus knot. The blue conformation on the right is the same knot but in the T(7,2) torus knot conformation.

Thingiverse link: http://www.thingiverse.com/make:82264

Settings: Printed on a MakerBot Replicator 2 with our custom knot slicing settings to minimize supports. Printing the knot on its side results in far, far less support material than printing knot horizontally.

Technical notes, OpenSCAD flavor: This knot was printed by JMU student Taylor Meador, who used a modified version of the OpenSCAD code for our trefoil torus knot models from Day 150 (thanks as always to kitwallace).

$fn=24;

/*
// trefoil as the torus knot T(7,2)
// http://mathworld.wolfram.com/Torus.html
// take parameterization of torus (u,v)->R^3
// and let u=2t, v=3t
// scaled to 40mm before tubifying
function f(t) =
[ 3.9*(3+1.6*cos(7*t))*cos(2*t),
3.9*(3+1.6*cos(7*t))*sin(2*t),
3.9*(1.6*sin(7*t))
];
// create the knot with given radius and step
tubify(1.6, 1, 360);
*/

module tubify(r, step, end) {
for (t=[0: step: end+step]) {
hull() {
translate(f(t)) sphere(r);
translate(f(t+step)) sphere(r);
}
};

Day 285 - Seifert surface of 6_3

Today we continue with the knot conformations collection that we started on Day 266. (See also Day 267, Day 268, Day 269, Day 272, Day 273, Day 275, and Day 276.) Today's knot is 6_3. Along with the usual conformation of 6_3 we printed a confirmation with a Seifert surface. A Seifert surface is a surface whose boundary is the knot, so if you trace along the edge of the red model you will trace out a conformation of the knot 6_3.

Thingiverse link: http://www.thingiverse.com/make:82226

Settings: Printed on a Replicator 2 with the model on its side, to minimize supports.

Technical notes, math flavor: This knot was made by Jonathan Gerhard, who has this to say about the math behind his model: A Seifert surface of a knot is an orientable, simply connected surface with a knot as its boundary. There are infinitely many different Seifert surfaces for any given knot. This particular example is a “Ribbon” configuration of a surface with the 6_3 knot as its boundary. An algorithm to create such a surface from any knot was first given by Herbert Seifert in 1934, and since then many different knot invariants, things that don’t change no matter how the knot is represented, have been found in relation to these surfaces.

Technical notes, SeifertView/Blender flavor: To make the Seifert surface model, Jonathan used the wonderful program SeifertView, created by Jack van Wijk from the Department of Mathematics and Computer Science of Eindhoven University of Technology. The freely-available version of SeifertView does not include an STL exporter, but Dr. van Wijk was kind enough to send Jonathan a special copy of the program that would allow STL export for this project. After exporting from SeifertView, Jonathan did some post-processing in Blender to thicken the surface. Here is his walkthrough of what he did to make today's model:

To begin with, you need to download a special version of SeifertView that allows exporting. It’s not currently online, so if you need it, contact me at gerha2jm@dukes.jmu.edu. On the right-hand side of the SeifertView window there is a menu in which you can click on 6_3. Then on the bottom there will be an option to change it into a Ribbon surface and an option to Smooth the surface. Unclick the Smooth button after you’re satisfied with the smoothness.



Now you'll want to go to Misc. in the upper right-hand corner, choose Advanced, and choose Save Geometry under option two.





Now go in Blender, go to File/Import/OBJ. On the right-hand side there will be a small row of icons including a camera, sphere, etc. Choose the wrench, click Add Modifier, and then choose Solidify.



Change Thickness to 0.03, and Offset to 0. Make sure High Quality Normals and Fill Rim are checked. (Note for future prints: Our model had some problems with its boundary when printing; it may help to flip the normals at this point and see if that helps solve the problem.)



Finally, hit Apply, then go to File/Export/STL.

Day 284 - Friday Fail: Using failure as a design element, or Psychoalphadicsobetabioaquadoloop

Today we printed peetersm's Customizable DrooLoop Flowers on Thingiverse. The one on the left has the "windswept" look that he describes in his fan control video, caused by the printer fan blowing the strands to the right as they cooled. The one on the left was printed with the fan off, which helped a lot but which made the model generally too hot and gloopy as it printed.

Thingiverse link: http://www.thingiverse.com/make:81447

Settings: MakerBot Replicator 2 on the recommended .2mm/standard layer height for this model. I couldn't figure out how to turn the fan off for just the petal loops (I could have it start off and then turn on at a specified layer, but I needed the opposite), so for the second flower head I made a custom profile where the fan was off all of the tie.

Technical notes, printing flavor: Here's a video showing the ingenious way that this model is printed; the flower head is printed upside-down, like a cup, and then the printer nozzle swings loops out into empty, unsupported space and back again. It's great fun to watch and makes really organic-looking shapes. Normally printing an unsupported overhang would cause a failure, but here that failure is built into the design itself.

Technical notes, musical flavor: To swim underwater and not get wet, let Parliament show you how to Aqua Boogie.

BONUS FAIL: I'm completely failing to keep up with time, and posted this over a week late! We move on July 1 and hopefully after that I can be caught up and on track each day. If you're reading this in the future when I'm already caught up then please pretend that this paragraph isn't here and that everything was posted in a timely fashion every single day.

Day 283 - Everything will be forever centered around Pokemon

One last print for C's Pokemon addiction: jessed's Pokemon Deck Box on Thingiverse.

Thingiverse link: http://www.thingiverse.com/make:81427

Settings: MakerBot Replicator 2 with .3mm/low and a raft, on blue painter's tape on a glass build platform.

Technical notes, printing flavor: For some reason large, flat things tend to print out all stringy on my Replicator 2. This isn't a new thing; we've had this problem since at least as far back as when we were printing Menger Coasters on Day 121 and Day 122. The situation improves if I switch to .2mm layer resolution, but does not go away entirely. The weird thing is the the rafts print perfectly, with flat, beautiful surfaces. If you know why this happens and what setting or technique will help, please let me know!

Day 282 - Must print all the Pokemon

Can you print just two Pokemon models for a 9-year-old? No. Two is not enough. You must print many, many Pokemon and then also print a full set for a friend's birthday. Today we are joined by FLOWALISTIK's Low-Poly Squirtle and Low-Poly Totodile models from Thingiverse. I'm really impressed with all four of these models. They are each designed to print perfectly without support and utilise extremely efficient choices of low-poly faces. Great design work by FLOWALISTIK, just please don't make me print any more of these right now.

Thingiverse link for (blue) Squirtle: http://www.thingiverse.com/thing:319413
Thingiverse link for (red) Totodile: http://www.thingiverse.com/thing:341719

Settings: Replicator 2 on .3mm/low, as usual.

Day 281 - Low-Poly Charmander and Bulbasaur

Pokemon fever has recently gripped my son's group of friends and now everything is about Pokemon cards more cards gotta get the best cards. As a surprise I printed FLOWALISTIK's lovely Low-Poly Charmander and Low-Poly Bulbasaur models for C, to celebrate his last week of school. These prints are expertly designed with about the lowest poly/face count that a model could have while still evoking Charmander and Bulbasaur. Very cool!

Thingiverse link for (green) Bulbasaur: http://www.thingiverse.com/thing:327753
Thingiverse link for (orange) Charmander: http://www.thingiverse.com/thing:323038

Settings: MakerBot Replicator 2 on .3mm/low with a raft, on blue tape on glass.

Day 280 - USAMO champion prints

Today I had the pleasure of meeting the 2014 USA Mathematical Olympiad champions at their awards celebration at the headquarters of the Mathematical Association of America in DC. We kicked off the day with a 3D-printing workshop. The students worked in four teams to design objects that would be printed later in the day. Most of the students had no design experience at all, but in under an hour they had collaborated to design some great things:

Three of the four models were made in Tinkercad. The spheres and half-spheres were made while the students learned how to use the Align and Hole tools. The figures with arms in the air were designed with extensive use of the Ruler tool and hand-calculated distances. The rockets were a minor miracle, as the students had decided to make one rocket that fits inside another and had to make a good guess for the amount of clearance/tolerance. They only had one try to make that guess, but they hit it square on the nose! The small rocket clicks into the large rocket beautifully.

The twisted square pyramid was made in OpenSCAD by a group in which one student had done some preliminary work (see Day 279). After a back-of-the-napkin calculation and some fights with compiling errors, this is what they made:

At the time I was helping all four groups and so didn't have a chance to ask the students about their construction, so let's take a moment to deconstruct it now. Their model is clearly a stack of rotated squares, each higher than the other and with corners on the edges of the supporting square. The part that needs calculating is determining how much to scale each square so that its corners align with the square below. From the students' code we can see that they are using a scaling factor sc determined by the ratio of the sum of the cosine and the sine of the angle of rotation. Why did they do that? Using some basic trigonometry we can draw out the following:

Once the picture is drawn there isn't much to do; the only thing you have to start with is the angle alpha and the original side length of 1. With a little trigonometry you can figure out the lengths of the legs a and b in the diagram, but what you really want it is the new side length h. The key insight is to realize that a + b = 1 so that you can solve for h, which becomes the scaling factor.

The USAMO students are some of the smartest, quickest math students in the nation. The top scorers will go on to represent our country in the International Mathematical Olympiad. They will go to college pretty much wherever they want to. They've worked amazingly hard to get to the level they are at, including taking extra courses and training workshops from organizations like the Art of Problem Solving. When they see a problem to solve they dive in fearlessly. They are curious, relentless, driven. Obsessive, even. In other words, they already think like mathematicians. Most importantly, like all mathematicians, they are experts in something that most people are terrible at, and it's not what you think it is; it's not calculating, or reasoning, or number sense, although they probably have all that as well. It's being able to be WRONG. To fail. To be stuck, confused, and lost. And then to get back up again and find another way around the problem.

One reason I was particularly excited to run a 3D-printing workshop with the USAMO champions was because I knew that most of them would have tons of mathematical experience, but no experience at all with 3D printing or design. These students are used to being the best. Not the best in their class or the best in their school, or even the best in their state. The best in the country. And competing with the best in the world. They are used to success. But in a 3D-printing workshop the playing field is level again, and the USAMO students struggled with basic alignment issues, design problems, and coding syntax just like all my other 3D students do.

Sometimes in my job as a math professor I see students who were rock stars in high school burn out once they get to college and are faced with new mathematics that they don't already know how to do. Those students somehow go from being experts at failing and problem-solving to being unable or unwilling to be stuck or feel stupid. The USAMO champions are at the top of their game and I wanted to remind them that they can still try new things and fail when they have to. And they did a great job of it. :)

UPDATE: Katherine Merow wrote a nice article for the MAA News about this called USAMO Winners Celebrated - and Challenged.