THE LIGHTER SIDE OF MATHEMATICS.
A BOOK on mathematica does not, at first sight, appear an attractive Christmas gift. Even enthusiastic mathematicians who agree with " Lewis Carroll" that "ouch a theorem as the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the aides' is as dazzlingly beautiful now as it was in the day when Pythagoras first discovered it, and celebrated its advent, it is said, by sacrificing a hecatomb of oxen," do not, we imagine, usually give books of problems to one another as souvenirs at the festive season. But we think Mr. Henry Dudeney's Amusements in Mathematics will prove an exception. True, it is possible, as Mr. Dudoney suggests, that "some few exceedingly sober-minded mathematicians who are impatient of any terminology in their favourite science but the academic" may object to "the elusive x and p' being presented in a more popular dress and introduced with flippant phraseology." as the writer deprecatingly describes it. To the majority of students of a "dismal science," however, we believe the book will be as welcome as to the general reader. Mr. Dudeney is well known as the author of many problems and" maths. matical puzzles" which have appeared in various magazines and newspapers. These problems and their solutions have been collected and published in book form, together with some new ones and "a few old puzzles that have interested the world for generations" There is one class of readers to whom the book should be not only an amusement but a revelation. We refer to those people for whom the science of mathematics represents something profoundly mys. terious, something expressed solely in curious symbols and cabalistic signs, and it thereby removed to a remoteness of inscrutability which they can never hope to approach, and certainly never to penetrate. It is impossible for them to conceive of it as anything so normal as arithmetic. The multiplication-table is a friendly thing, but when snot in mathematical formulae it is a nightmare. They are like the children at a certain school who were set a problem which, though quite simple in itself, was stated in purposely elaborate• terms. It began : "These Spanish muleteers were seated under an um- brageous oak tree," and the phrasing so terrified the children that not one of them attempted a solution. Let any such person get Mr. Dudeney's book, for hem he will find mathematics in undress, as it were, and in a familiar, even a merry, guise I Let him put away all thought of equations and theorems, segments and axioms, the hypotenuse and the isosceles triangle, regard the book as a collection of puzzles, and set himself to work out, say. "How many minutes is it until eix o'clock if fifty minutes ago it eras four times as many minutes past three o'clock ? " He may work it out by any method he chooses, and Mr. Dudeney will have nothing for him but sympathy and a solution written in untechnical and amity comprehended English. And all the time he may reflect that he is actually achieving what he thought to be the impossible and working at mathematics. There are any number of pleasantly worded puzzles for him to ponder. Here is a study " Academic Courtesies" which conjures up a delightful picture of juvenile deportment :—
" In a certain mixed school, where a special feature was made of the inculcation of good manners, they had a curious rule on assembling every morning. There were twice as many girls as boys. Every girl made a bow to every other girl, to every boy, and to the teacher. Every boy made a bow to every other boy, to every girl, and to the teacher. In all there were nine hundred bows made in that model academy every morning. Now, can you say exactly how many boys there were in the school I If you are not very careful, you are likely to get a good deal out in your calculation."
And what more amusing way of being a mathematician could be Invented than by trying to discover how a square pen containing seven pigs can be intersected with three straight fences so as to enclose every pig in a separate sty • mmuonests Ia Mathew...gm By Henry Ernest Dadeney. London: T. Nelson and Coo. ler. es. net.)
Mr. Dudeney provides for all tastes. There are chessboard problems; geometrical problems, magic squares, mazes ; moving-counter problems which include several intricate railway puzzles, and also the Grasshopper puzele, which is said to have been a great favourite among the young apprentices of the City of London in the sixteenth and seventeenth centuries ; route problems for cyclists and motor- isle ; puzzle games ; and at the end, in a little group of unclassified problems, is a study in deduction which will delight the heart of the embryo Sherlock Holmes. Some of the problems, as Mr. Dudeney himself suggest., are more in the nature of " catehes " or word. traps than legitimate mathematics ; but, if any justification Is needed, they certainly, as he claims, tend to the cultivation of observation and of exactitude and caution in expression.
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