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View Poll Results: Is this a useful construction?  
Yes  1  9.09%  
No  0  0%  
There are other ways  3  27.27%  
This method is wrong  7  63.64%  
Voters: 11. You may not vote on this poll 
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April 12th, 2012, 04:03 PM  #11  
Senior Member Joined: Feb 2010 Posts: 632 Thanks: 103  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
 
April 12th, 2012, 10:09 PM  #12  
Senior Member Joined: Aug 2011 Posts: 333 Thanks: 8  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
Figure on page 2 of the paper "Tracé d'un angle quelconque" : http://www.scribd.com/JJacquelin/documents . Last edited by skipjack; February 18th, 2017 at 05:17 AM.  
April 16th, 2013, 12:48 PM  #13  
Newbie Joined: Apr 2012 Posts: 2 Thanks: 0  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
i have constructed a perfect 20 degree by jst compass and ruler..... and i checked the construction accuracy on autocad too  
April 16th, 2013, 06:45 PM  #14 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Constructing a 20 Degree Angle using Compass and Ruler O
"2. Step 2:Keeping your compass wide open with the same length..." You violate the rules in your step 2, the compass must collapse when lifted off the page. 
April 19th, 2013, 07:00 AM  #15 
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Constructing a 20 Degree Angle using Compass and Ruler O
It can't be done. As an amateur origami artist, I know a little something about geometry. The most you can get down to is 12 degrees. http://www.flickr.com/photos/85937466@N ... 2639808715 I posted my $100 challenge on the Origami Forum for a 12 degree angle, and only 1 person came up with the solution. http://www.orime.de/downloads/origami3 ... degree.pdf http://www.flickr.com/photos/85937466@N ... 2639808715 Once you have 12 degrees, you can bisect it. To 6, to 3. And that's it for whole numbers. You can't get down to 1 without neusis. To construct a 20 degree angle you have to trisect a 60 degrees angle, which can't be done without neusis. http://www.flickr.com/photos/85937466@N ... 3074235305 Tom Hull's origami method of angle trisection. Performed by me. http://www.flickr.com/photos/85937466@N ... 3074235305 https://www.math.lsu.edu/~verrill/origami/trisect/ 
April 19th, 2013, 08:41 AM  #16  
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
Imprecision from analogtodigital is perfectly acceptable to me, because the method is correct, the imprecision is in the limitation of the definition of the instrument. Digitaltoanalog is fake, and you don't learn anything, you don't have any insights into the relationships of things. I call analog methods "The Definition of Definition". An example of an analog technique, angle trisection. http://www.flickr.com/photos/85937466@N ... hotostream On my challenge: viewtopic.php?f=13&t=39806#p163169 I specifically put in a no digitaltoanalog fakery clause. Last edited by skipjack; February 18th, 2017 at 05:20 AM.  
April 19th, 2013, 04:01 PM  #17 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Constructing a 20 Degree Angle using Compass and Ruler O
Anyone interested in deriving exact values of sines and cosines of special angles of the form 3k for integer k should look at the instructional video below. http://www.youtube.com/watch?v=kb_HyCThxE0 The whole video is extremely valuable but I would like to highlight a few things pertinent to finding exact values of special angles that are integer multiples of 3. 1) At time index 12:30 Ptolemy's Theorem is nicely derived. 2) At time index 22:00 exact values of some special angles are derived using triangles and addition/subtraction formulas for sines and cosines. Examples: 75, 60, 45, 30, 15. 3) Shortly after that, Ptolemy's Theorem is used to derive exact value of sin(18°) and once you have that sin(3) can be derived using subtraction formula sin(18  15) = sin(3). I strongly recommend looking at the entire instructional video, 30 minutes well spent. Question for [color=#0000FF]long_quach[/color], have you ever used Ptolemy's Theorem in your origami constructions? Last edited by skipjack; February 18th, 2017 at 05:22 AM. 
April 20th, 2013, 06:41 AM  #18  
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
Excellent video by the way.  
April 20th, 2013, 06:44 AM  #19  
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
viewtopic.php?f=13&t=39895#p163585 Last edited by skipjack; February 18th, 2017 at 05:24 AM.  
April 20th, 2013, 11:38 AM  #20  
Banned Camp Joined: Feb 2013 Posts: 224 Thanks: 6  Re: Constructing a 20 Degree Angle using Compass and Ruler O Quote:
http://www.flickr.com/photos/85937466@N ... otostream/ How old are you atharvjoshi? Telling us something about yourself tells us about the question you pose. Don't take this "failure" the wrong way. Genius is NOT coming up with the solution. Genius is coming up with the question. How did you realize that 20 degrees is not so easy to construct? You attempt didn't work, but your question led to the question of the validity of the the protractor. How the heck was it constructed? We take it for granted that a protractor is easily constructed, but it's not. Don't let failed solutions discourage you. Genius is coming up with the questions, in noticing things out of the ordinary.  

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angle, compass, constructing, degree, ruler 
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