If you have ever solved a mathematical puzzle, played any game in which numbers were used, learned a number trick, or played ticktacktoe, you have indulged in a type of mathematical recreation. In general, these recreations share three characteristics: first, they are mathematical or logical; second, they are fun; third, they all appear to be quite useless.
The first two characteristics require no support, but some might ask why anyone should indulge in anything that is of no practical value. An indirect defense may be built up from the fact that the most staid mathematics and engineering journals publish some material that is strictly recreational in nature, giving the amusements a kind of endorsement.
Moreover, a very cursory examination will disclose a few interesting facts about the utility of recreational mathematics. Prime numbers, for example, have no practical value. It may be decades, if ever, before such a use for them will be found. However, the study of prime numbers and their properties has filled many a gap in the field of number theory, that mathematical discipline which studies the basic properties of all numbers. Magic squares have been involved with superstitious beliefs and proven an interesting source of amusement for centuries. They, too, offer practical rewards for the agricultural and nuclear scientist. The study of the patterns of certain types of magic square has shown how to reduce the number of experiments required to obtained growth and radiation data. The classic Moebius strip has been used for conveyor belts that
last twice as long as conventional belts. Indeed, the B. F. Goodrich Co. has obtained a patent for this particular use. Many areas of recreational mathematics still seem to be useless, but who can say what next year or the next decade will bring?