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GEOMETRICAL
PROBLEMS.
"God geometrizes
continually."
PLATO.
"There is no study," said Augustus de Morgan, "which presents so simple a
beginning as that of geometry; there is none in which difficulties grow more
rapidly as we proceed." This will be found when the reader comes to consider the
following puzzles, though they are not arranged in strict order of difficulty.
And the fact that they have interested and given pleasure to man for untold ages
is no doubt due in some measure to the appeal they make to the eye as well as to
the brain. Sometimes an algebraical formula or theorem seems to give pleasure to
the mathematician's eye, but it is probably only an intellectual pleasure. But
there can be no doubt that in the case of certain geometrical problems, notably
dissection or superposition puzzles, the ęsthetic faculty in man contributes to
the delight. For example, there are probably few readers who will examine the
various cuttings of the Greek cross in the following pages without being in some
degree stirred by a sense of beauty. Law and order in Nature are always pleasing
to contemplate, but when they come under the very eye they seem to make a
specially strong appeal. Even the person with no geometrical knowledge whatever
is induced after the inspection of such things to exclaim, "How very pretty!" In
fact, I have known more than one person led on to a study of geometry by the
fascination of cutting-out puzzles. I have, therefore, thought it well to keep
these dissection puzzles distinct from the geometrical problems on more general
lines.
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