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August 11th, 2014, 05:38 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, 06:43 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, 07:37 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, 07:39 PM  #4 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  How to use Oripa 
August 11th, 2014, 07:51 PM  #5 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  
August 11th, 2014, 08:25 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 secondlargest root of $x^633x^4+27x^23$ which is the square root of the secondlargest root of $x^333x^2+27x3$. 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, 08:55 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 08:57 PM. 
August 11th, 2014, 10:32 PM  #8 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  
August 12th, 2014, 06:41 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  I don't know how I could know that. 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, 07:06 AM  #10 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  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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