Harry Lindgren, Greg Frederickson, "Recreational Problems in Geometric Dissections and How to Solve Them"
English | 1972 | ISBN: 0486228789 | PDF | pages: 212 | 6,3 mb
It was Hilbert (or was it Bolyai and Gerwien?) who first proved that any rectilinear plane figure can be dissec ted into any other of the sam e area by cu tting it into a finite number of pieces. (It is na tural to ask, did we need a Hilbert to do that?) In the proof no account is taken of the number of pieces-one wants only to show that it is finite. But the main in terest of dissections as a recreation is to find how to dissect on e figure into ano ther in the least number of pieces. In a few cases (v ery, very few) it could perhaps be rigorously proved that the minimum number has been attained, and in a few more one can feel morally certain ; in all the rest it is possible that you may find a dissection that is be tter than those already known, or may even find a new kind of dissec tion . The subject is nowhere near exhaustion . In this respect it compares -favora bly with many recreations of the algebraic kind; magic squares, for instance, have been worked almost to death.
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