In the Russian translation of this book published in the U.S.S.R. an additional appendix was added by the mathematician I. M. Yaglom, establishing the irrationality of almost all values of the trigonometric functions for rational degree arguments. It seemed to me that such an appendix should also be included in the English language edition, and I am grateful to Random House for agreeing at once to such an addition. Thus in this printing there is a new Appendix D, TRIGONOMETRIC NUMBERS, establishing the same results as in the Russian version, but with simpler methods I believe. A few minor changes have also been made, mostly clarifications in wording. I am indebted to several correspondents who suggested the improvements.