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Cinq Carve (Posted on 2014-04-25) Difficulty: 4 of 5
Consider a rectangular piece of paper ABCD with AB ≠ AD

Show how you can fold this piece of paper into five pieces of equal area.

*** Using any given instrument like straightedge, compass, protractor, ruler etc. is NOT permissible.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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re(3): a solution | Comment 4 of 7 |
(In reply to re(2): a solution by Jer)

Jer:


Well, I guess I don't understand your approach to getting parallel creases.  Inside the parentheses, you say "For greater accuracy in the four folds, I can be folded to points on the crease IB such that the new creases formed pass through each of H, G, F and E."  When I actually try it, that doesn't seem to work.  In order to get a crease that passes through H, you need to join a point that is an extension of IB and off the page to another point on IB.  But that's not really possible.

My approach to parallel creases is to create a new crease that is the perpendicular bisector to IB, which is done by folding I to B.  Call that crease JK, where J is a point on BC.  Then fold J to a point on JK such that the new crease goes through H.  That newly formed crease is parallel to IB.  The only problem with this, when I try it, is that I cannot form the parallel crease through point E if E F G and H are on the short side of the rectangle.  Which is why I need to create my first crease by folding the short side less than 1/5 of the way towards the other short side.

  Posted by Steve Herman on 2014-04-26 23:09:05
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