On Saturday, February 20, 2016, Erich Friedman <erichfriedman68@gmail.com <javascript:_e(%7B%7D,'cvml','erichfriedman68@gmail.com');>> wrote:
an interesting idea. although you obviously meant a circle of AREA 2, not radius 2.
Actually, I meant to say FOUR circles of radius 1. You can for instance radially divide a disk of radius 2 into lots of approximately triangular wedges, divide each wedge into four roughly triangular pieces, and rearrange the pieces to form four approximate disks of radius 1. how would you measure how good the approximation is? the smallest inradius
of the two sets of rearranged pieces? the largest circumradius of the two sets of rearranged pieces? the minimum area of overlap of a unit disk with these sets?
I'm not sure what the most natural measure is. All of Erich's suggestions sound good. Jim
erich
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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