Mathematical Recreations and Essays

Excerpt from Mathematical Recreations and Essays The earlier part of this book contains an account of certain Mathematical this is followed by some Essays on subjects most of which are directly concerned with historical mathematical problems. I hasten to add that the conclusions are of no practical use, and that 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 say that many of the questions discussed 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. A great deal of new matter has been added since the work was first issued in 1892, but insertions made since 1911, when the book was stereotyped, have had to be placed where room for them could best be found. The book is divided into two parts, but in both parts I have excluded questions which involve advanced mathematics. The First Part now consists of ten chapters, in which are described various problems and amusements of the kind usually termed Mathematical Recreations. Several of the questions mentioned in the first five 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 left them in the absence of such a work, I thought it better to insert them and trust to the judicious reader to omit them altogether or to skim them as he feels inclined.

H. S. M. Coxeter: Through the Looking Glass
Harold Scott MacDonald Coxeter (1907–2003) is one of the greatest geometers of the last century, or of any century, for that matter. Coxeter was associated with the University of Toronto for sixty years, the author of twelve books regarded as classics in their field, a student of Hermann Weyl in the 1930s, and a colleague of the intriguing Dutch artist and printmaker Maurits Escher in the 1950s.

In the Author's Own Words:
"I'm a Platonist — a follower of Plato — who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."

"In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways."

"Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry."

"Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." — H. S. M. Coxeter