Mathematical Recreations and Essays · W. W. Rouse Ball

Preface to the First Edition

1 of 16 · 2 min of reading

The following pages contain an account of certain mathematical recreations, problems, and speculations of past and present times. I hasten to add that the conclusions are of no practical use, and most of the results are not new. If therefore the reader proceeds further he is at least forewarned.

At the same time I think I may assert that many of the diversions--particularly those in the latter half of the book--are interesting, not a few are associated with the names of distinguished mathematicians, while hitherto several of the memoirs quoted have not been easily accessible to English readers.

The book is divided into two parts, but in both parts I have included questions which involve advanced mathematics.

The first part consists of seven chapters, in which are included various problems and amusements of the kind usually called mathematical recreations. The questions discussed in the first of these chapters are connected with arithmetic; those in the second with geometry; and those in the third relate to mechanics. The fourth chapter contains an account of some miscellaneous problems which involve both number and situation; the fifth chapter contains a concise account of magic squares; and the sixth and seventh chapters deal with some

unicursal problems. Several of the questions mentioned in the first three chapters are of a somewhat trivial character, and had they been treated in any standard English work to which I could have referred the reader, I should have pointed them out. In the absence of such a work, I thought it best to insert them and trust to the judicious reader to omit them altogether or to skim them as he feels inclined.

The second part consists of five chapters, which are mostly historical. They deal respectively with three classical problems in geometry--namely, the duplication of the cube, the trisection of an angle, and the quadrature of the circle--astrology, the hypotheses as to the nature of space and mass, and a means of measuring time.

I have inserted detailed references, as far as I know, as to the sources of the various questions and solutions given; also, wherever I have given only the result of a theorem, I have tried to indicate authorities where a proof may be found. In general, unless it is stated otherwise, I have taken the references direct from the original works; but, in spite of considerable time spent in verifying them, I dare not suppose that they are free from all errors or misprints.

I shall be grateful for notices of additions or corrections which may occur to any of my readers.

W.W. ROUSE BALL

0=Trinity College, Cambridge. 1= to0February, 1892. 0 1

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