## Solving cubic equations with origami

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### Solving cubic equations with origami

(WARNING: this will not make much sense if you do not know what cubic equations are)
Not sure if this is the correct place to post this, but I would like to share a fascinating application of origami to math that I have just learnt of. Basically, folding can be used in conjunction with a pen and a ruler to solve cubic equations (3rd degree polynomials) of the form ax³ + bx² + cx + d = 0

Here is the video I learnt it from:

I find it interesting that using folding is the only way cubic equations can be solved geometrically on paper. A compass and straight edge cannot do this. I highly recommend you watch the above video and give it a go yourself if you are interested by both math and origami. It takes a bit of getting the hang of to do yourself, but the video explains it pretty well. This one also helps: https://www.youtube.com/watch?v=6MZEBB24Irg

Apparently, through origami is also the only way you can trisect an angle. I wonder what other applications origami has to math?
See some photos on my flickr

Merlyngami
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### Re: Solving cubic equations with origami

Is it considered a cubic equation if you need to reflect two points onto a line simultaneously?

I don't know if you're familiar with the Huzita-Hatori (Huzita-Justin) axioms, but they're pretty fascinating and also relevant to this video.
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Baltorigamist
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### Re: Solving cubic equations with origami

Baltorigamist wrote:I don't know if you're familiar with the Huzita-Hatori (Huzita-Justin) axioms, but they're pretty fascinating and also relevant to this video.

It is Axiom 6, which I just implemented in Origami Draw, my app for iPhone and iPad (see this thread). Here is an animated GIF showing the construction of all three roots:

and some static images:

It's easier than drawing by hand!
OriGenes
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### Re: Solving cubic equations with origami

Here is an interesting paper I just found which covers an analogous topic in simpler(?) terms. It's definitely an interesting read.
After the fall, we rise.

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Baltorigamist
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### Re: Solving cubic equations with origami

Wow, this is fascinating. Thanks Baltorigamist, I tried to find a paper on the beloch square but couldn't (until now). Sorry if this has been asked origenes, but will oridraw ever be ported to android?
See some photos on my flickr

Merlyngami
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