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Mathematics that you can touch

These last months have been intense, so intense I needed a bit of a distraction. I’ve always felt some kind of curiosity for the world of 3D printing and, as I’ve said in different occasions, I always push KAlgebra to the limit when I have the occasion.

I had been researching, I’ve never had a 3D printer and I probably won’t have one in years, but I still wanted to figure out how to get do something there. First, I went through many 3D printing services and looked through the different supported formats. To be honest, I implemented the one that looked the simplest, it happened to work quite similar to how OpenGL works internally, so it seemed like a safe bet.

Once I had a working export algorithm, I chose an extremely good looking plot (thanks Percy ;-)) and then I uploaded it over to one of those 3D printing services. The website showed me a preview, it seemed like their software understood the format, so it looked like my job was done. I fiddled with it to get it printed in a reasonable size and submitted it to print and send. For the curious, here’s the formula I used:

piecewise { x^2+y^2+z^2<35 ? 2-(cos(x+(1+5^0.5)/2*y)+cos(x-(1+5^0.5)/2*y)+cos(y+(1+5^0.5)/2*z)+cos(y-(1+5^0.5)/2*z)+cos(z-(1+5^0.5)/2*x)+cos(z+(1+5^0.5)/2*x)), ? 1 } = 0

A couple of weeks later a box arrived to our office. To be honest, it was a bit weird. I was very excited, but then nobody else was when I showed it. Because it's math I guess, and it's boring. I felt a bit like when I used to spend my nights hacking KAlgebra around then show it around. Anyway, I'll say it. A 3D plot, in my hands, to play with them. How cool is that? :D

** crickets **


Now I'm sure you're excited and willing to try it. It will be available in the next version of KAlgebra, that will be released in the KDE Applications 2014.12, which by the way will be the first KAlgebra release based on Qt5 and KF5, and will be featuring many other new features.
And of course, it's free software developed in an open community! If you're feeling adventurous or you just know how to build KDE software, feel free to pull analitza and kalgebra repositories and give it a try! :)


  1. Alex Elsayed

    A quick modification of the equation might have printed better:

    piecewise {
    x^2+y^2+z^2<5 ? 0,
    x^2+y^2+z^2<35 ? 2-(cos(x+(1+5^0.5)/2*y)+cos(x-(1+5^0.5)/2*y)+cos(y+(1+5^0.5)/2*z)+cos(y-(1+5^0.5)/2*z)+cos(z-(1+5^0.5)/2*x)+cos(z+(1+5^0.5)/2*x)),
    ? 1
    } = 0

    This way, the inner sphere is large enough to be "caged", which gives a nice result.

  2. duiliob

    That’s awesome! What format did you use? keep up the good work!

  3. apol

    #1 Thanks! Will take it into account!!

    #2 Uh sorry I forgot to mention, it’s X3D.

  4. Thomas Pfeiffer

    This is indeed awesome, especially for educational purposes!
    How much more fun would math courses be if students could print the graphs they created? I’m sure competitions for who creates the function that produces the coolest object when its graph is printed would emerge soon.
    We have to really advertise that to schools, “Mathematics you can touch!” sounds like a great slogan for that!

  5. Jan

    I think I’ll ask what everyone is thinking but not asking… is your cat named Qwerty?? xD

  6. apol

    #4 😀 😀 😀

    #5 Yes, Qwerty. The full name would be Qwerty Uiop, of course. But we call him Qwerty because it’s shorter. 🙂

  7. Jan

    Cool name! xD

  8. Adam S

    Cat eating math. So awesome.

    I think this idea is really cool, and I think you can take this way further. A function that looks (to the unaware) like a hollow ball is sort of boring. 3D printers can make any conceivable shape. It doesn’t have to be periodic or loosely spherical. I don’t have any functions in mind, but could you make something that has the appearance of being much more complex and intricate? Like these fancy fractals:

  9. Alok

    Could you please point which 3d printing website did you use?

  10. apol

    #9 I used

  11. GreatEmerald

    That’s a really nice cat!

    Maths? What maths? 😉

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