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I have a rectangular piece of paper with a circle printed on it. I also have a handy-dandy writing utensil. How can I locate and mark the center of the circle?

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Here's some technicalities:

  • The paper is "infinitely thin," perfectly foldable, opaque, and a perfect rectangle. The circle is also perfect.
  • The circle does not overlap, extend past, or touch the edges of the page.
  • The paper can be any size rectangle and the circle can have any size radius, but these are out of our control.
  • The edges of our folded page serve as our straightedge. We can also use the lines generated by the creases.
  • One thing that we cannot do is simply guarantee well in advance that our folds occur at any particular angle. (I've found a really simple solution that involves this.)
  • Our writing utensil is a tool of ridiculous precision (and accuracy).
  • We don't have any access to third party services or tools.

Once the simplest version of this puzzle is solved, I am very interested in how we can change the puzzle and have it remain solvable.

  • Can it be solved if the edges of the circle are allowed to touch the edges of the page?
  • Can it be solved if we are not allowed to create tangents to the circle?
  • Can it be solved if the paper is infinitely tall and wide, so that we only have access to one corner and two edges?

This question is somewhat inspired by / based off of a similar puzzle which allowed the use of book, but which did not specify a rectangular piece of paper.

  • 0
    What are the conditions of the paper?density, type, these things?2012-10-15
  • 0
    http://math.stackexchange.com/questions/56457/determine-the-centre-of-a-circle/153896#1538962012-10-15

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