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August 11th, 2014, 04:38 PM   #1
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$1,000 USD Prize - Origami Ellipse

Rebecca Gieseking created a very elegant origami model.



https://www.flickr.com/photos/rgieseking/9595911874/

This is the crease pattern.


https://www.flickr.com/photos/rgieseking/9983312295/

I believe I figured out the neusis construction.



https://www.flickr.com/photos/85937466@N02/14622280160/

I will pay you $1,000 USD if you can figure out the algebraic solution.



https://www.flickr.com/photos/85937466@N02/14904355293/

Long Quach
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August 11th, 2014, 05:43 PM   #2
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Would you be more precise?
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August 11th, 2014, 06:37 PM   #3
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Find the exact distance between the 2 cosine waves, using algebra or algebraic construction. Download these files. Oripa is a program that folds a crease pattern.

GeoGebra
https://www.dropbox.com/s/fvirjxbefb...ll%20along.ggb

Oripa
https://www.dropbox.com/s/obsxq8p9ic...ll%20along.opx
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August 11th, 2014, 06:39 PM   #4
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How to use Oripa

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August 11th, 2014, 06:51 PM   #5
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Quote:
Originally Posted by CRGreathouse View Post
Would you be more precise?
Essentially make an origami model of this with a 40° degrees angle slice.

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August 11th, 2014, 07:25 PM   #6
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A 40 degree angle is certainly constructible by neusis/origami/etc. tan(40°) = tan(2π/9) is the second-largest root of $x^6-33x^4+27x^2-3$ which is the square root of the second-largest root of $x^3-33x^2+27x-3$.

I don't have enough faith in the offer to bother with the geometry (which I generally don't enjoy) or the tedium of constructing 12 pieces. But I encourage others to try.
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August 11th, 2014, 07:55 PM   #7
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Pi (π) is allowed. The circumference of the ellipse is allowed. Trigonometric functions are allowed. GeoGebra is allowed.

Last edited by long_quach; August 11th, 2014 at 07:57 PM.
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August 11th, 2014, 09:32 PM   #8
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Quote:
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I don't have enough faith in the offer to bother with the geometry (which I generally don't enjoy) or the tedium of constructing 12 pieces.
The prize is real. The math is real.

It's one piece with 12 divisions of 2π. Look at the picture.
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August 12th, 2014, 05:41 AM   #9
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Quote:
Originally Posted by long_quach View Post
The prize is real.
I don't know how I could know that.

Quote:
Originally Posted by long_quach View Post
It's one piece with 12 divisions of 2π.
Yes, exactly. It would be a pain to work with that. If I knew I'd get $1000 it would be worth my time and aggravation but I don't. However someone else might feel differently (or value their time differently) and I encourage any such to solve the problem.
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August 12th, 2014, 06:06 AM   #10
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Quote:
Originally Posted by CRGreathouse View Post
I don't know how I could know that.
You talk like a robot. How about it is so because it is my word.

Online Etymology Dictionary

"word"
The meaning "promise" was in Old English, as was the theological sense.

But to ease your limited robotic mind:





for this:


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