The main purpose of the book is to communicate a fundamental principle to the scientific world. The eventual impact of the subject matter is considered to be much wider than the readership of the preliminary accounts which have been published. The number principle at issue is known to be of wide general interest and the book has also been written to be accessible to nonspecialists. The potential readership should extend way beyond academic scientists.The discovery described in this book could be of seminal significance, also in other fields where the golden ratio is known to be of fundamental importance. The most obvious connection is with Fibonacci phylotaxis in the study of botanical growth and the number basis of DNA coding. In another context it may impinge on crystallographic periodicity and the structure of quasicrystals. These topics are beyond the scope of this book and hence it is all the more important that the power of number theory to describe physical systems be disseminated more widely.