Recreational Problems in Geometric Dissections and How to Solve Them

Recreational Problems in Geometric Dissections and How to Solve Them

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 numĀ­ber 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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