macaroni.ggb

Negative_Entropy
Negative_Entropy
618
0
Published 2021-02-24
GeoGebra machine that draws a seemingly 3D projection of a piece of macaroni.
This is basically a mechanical setup with two engines rotating, and a stick connected to one, sliding on the other and drawing with its end.
I calculated the parametric function path it follows, and it is something like:
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\left(3\cdot\sin\left(t\right)-\frac{20}{\sqrt{\frac{3\sin\left(t\right)-4\sin\left(1.55\cdot t\right)}{3\cos\left(t\right)-4\cos\left(1.55\cdot t\right)+10}^{2}+1}}\cdot\frac{3\sin\left(t\right)-4\sin\left(1.55\cdot t\right)}{3\cos\left(t\right)-4\cos\left(1.55\cdot t\right)+10},\ 3\cdot\cos\left(t\right)-\frac{20}{\sqrt{\frac{3\sin\left(t\right)-4\sin\left(1.55\cdot t\right)}{3\cos\left(t\right)-4\cos\left(1.55\cdot t\right)+10}^{2}+1}}\right)
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Throw this in www.desmos.com/calculator/ksjcpazwa9?lang=nl
with 0 to t to 200

Whats even more fun is to use a version with variables and add sliders for those vars
I reverse checked some of the cool shapes i got here in geogebra and they are all drawable
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\left(a\cdot\sin\left(t\right)-\frac{d}{\sqrt{\frac{a\sin\left(t\right)-b\sin\left(f\cdot t\right)}{a\cos\left(t\right)-b\cos\left(f\cdot t\right)+c}^{2}+1}}\cdot\frac{a\sin\left(t\right)-b\sin\left(f\cdot t\right)}{a\cos\left(t\right)-b\cos\left(f\cdot t\right)+c},\ a\cdot\cos\left(t\right)-\frac{d}{\sqrt{\frac{a\sin\left(t\right)-b\sin\left(f\cdot t\right)}{a\cos\left(t\right)-b\cos\left(f\cdot t\right)+c}^{2}+1}}\right)
a=3
b=4
c=10
d=20
f=1.55

Music:    • Leto Macaroni ft. Ninho Instrumental ...  
All Comments (11)
  • @Univercius
    IronException probably liked this a lot. Reminds me a bit of Fourier Series, and didn't realize that you could project 3D graphs into 3d like this. Either way, this is really cool.
  • @Icare433
    That's one seriously good edit....
  • @H4RD
    I'm just stunned ... It's so beautiful even if I don't even begin to comprehend the math behind that movement. Does it start repeating the pattern at any point or does it follow an infinite drawing pattern?
  • @capwithak7178
    Not sure what this was, but i can vibe to the music so it doesnt matter song name?