"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 æsthetic
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.