November 30th, 2017, 07:52 AM  #1 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2  origami
There is a proof that it can be a way to fold A4 page to a circle? Why not? Why yes? [This is the last question for today so sorry on the overflow] 
December 1st, 2017, 09:08 AM  #2 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2 
I think the number of folds that possible in A4 page is 28 folds. So the answer is no.

December 1st, 2017, 10:41 AM  #3 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2 
But what about unlimited folds?
Last edited by skipjack; December 1st, 2017 at 11:05 AM. 
December 1st, 2017, 11:13 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,248 Thanks: 1439 
Each fold produces a straight edge, but an approximation to a circle is possible by drawing a circle on the paper and then making folds as close to it as you can.

December 1st, 2017, 11:37 AM  #5 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2 
O.K. but only closely not accurate. The question is why?
Last edited by shaharhada; December 1st, 2017 at 11:41 AM. 
December 1st, 2017, 11:41 PM  #6 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2 
In my original question: cutting is forbidden. But if you can't answer with no cutting so give a solution to a minimum cutting operations.

December 2nd, 2017, 08:18 AM  #7 
Senior Member Joined: Nov 2011 Posts: 170 Thanks: 2 
Because there are no responses to this post, I think to give a little help as much I know. Probably, there is a formula or method that can help. If somebody know a formula for things like this, it can very helpful to develop this post. Thank you!!! Last edited by skipjack; December 3rd, 2017 at 04:23 AM. 
December 2nd, 2017, 10:50 AM  #8 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,091 Thanks: 2360 Math Focus: Mainly analysis and algebra 
I think that if you investigate curvature of spaces, you'll find that it's impossible because you need curved space to make curved folds and the paper is flat space.


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