My Math Forum $1,000 USD Prize - Origami Ellipse  User Name Remember Me? Password  Trigonometry Trigonometry Math Forum  August 11th, 2014, 04:38 PM #1 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6$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 $1,000 USD if you can figure out the algebraic solution. https://www.flickr.com/photos/85937466@N02/14904355293/ Long Quach  August 11th, 2014, 05:43 PM #2 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Would you be more precise?  August 11th, 2014, 06:37 PM #3 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6 Find the exact distance between the 2 cosine waves, using algebra or algebraic construction. Download these files. Oripa is a program that folds a crease pattern. GeoGebra https://www.dropbox.com/s/fvirjxbefb...ll%20along.ggb Oripa https://www.dropbox.com/s/obsxq8p9ic...ll%20along.opx  August 11th, 2014, 06:39 PM #4 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6 How to use Oripa August 11th, 2014, 06:51 PM #5 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6 Quote:  Originally Posted by CRGreathouse Would you be more precise? Essentially make an origami model of this with a 40° degrees angle slice.  August 11th, 2014, 07:25 PM #6 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms A 40 degree angle is certainly constructible by neusis/origami/etc. tan(40°) = tan(2π/9) is the second-largest root of$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.  August 11th, 2014, 07:55 PM #7 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6 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. August 11th, 2014, 09:32 PM #8 Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6 Quote:  Originally Posted by CRGreathouse 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. August 12th, 2014, 05:41 AM #9 Global Moderator Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Quote:  Originally Posted by long_quach The prize is real. I don't know how I could know that. Quote:  Originally Posted by long_quach 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.

August 12th, 2014, 06:06 AM   #10
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Quote:
 Originally Posted by CRGreathouse 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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