Take a unit square and cut out a sqrt(0.5) by sqrt(0.5) square out of one corner, exactly half the area. Cut up the L-shaped piece orthogonally and rearrange it symmetrically into another square. An infinite number of pieces is likely required.
Cut off the two arms from the L and arrange as bars, leaving a .121 by .707 gap to be filled by the material of a .293 by .293 square. Or scaled, a .414 by 2.414 gap by a unit square.
Slice two .121 by .293 bars and place them in the gap, leaving a .121 by .121 square to be filled by the remaining material of .0503 by .293. Again, scaled unit square filling .414 by 2.414.
Because of identical scaling, this can be repeated recursively forever.
No comments :
Post a Comment