This paper, "Scissor congruence" by Hirsch, Dubins, and Karush Israel Journal of Mathematics December 1963, Volume 1, Issue 4, pp 239-247 seems to address some aspect of this question, depending on how the question is defined. The first page: http://link.springer.com/article/10.1007/BF02759727#page-1 mentions rearranging one circle into four explicitly. (I don't have access to the whole paper, so if someone gets an electronic copy, I would appreciate getting a copy of that myself.) —Dan
On Feb 20, 2016, at 10:43 AM, James Propp <jamespropp@gmail.com> wrote:
Actually, I meant to say FOUR circles of radius 1.
Does anyone know of work that's been done on approximate dissection and recomposition of disks? For instance, dividing a disk of radius 2 into pieces and then rearranging the pieces to form an approximation to two discs of radius 1?
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