This book is devoted to anyone who is in search of beauty in mathematics, and mathematics in the beauty around us. Attempting to combine mathematical rigor and magnificence of the visual perception, the author is presenting the mathematical study of phyllotaxis, the most beautiful phenomenon of the living nature. The distinctive feature of this book is an animation feature that explains the work of mathematical models and the transformation of 3D space.The analysis of the phyllotactic pattern as a system of discrete objects together with the mathematical tools of generalized sequences made it possible to find a universal algorithm for calculating the divergence angle. In addition, it is serving as a new proof of the fundamental theorem of phyllotaxis and analytically confirming well-known ...

Does the field of evolution differ from other sciences? The author, a reviewer for a major medical journal, scrutinized hundreds of scientific references in evolutionary literature, adopting the same standards used for studies submitted for medical publication. The data show that there are two types of evolution, microevolution and macroevolution, with a clear boundary between them based upon the presence and absence of empirical evidence, respectively. The surprising results show that there is a universal disconnect between the data and the conclusions that claim to show the larger changes of macroevolution. The author reveals patterns of deviations from standard scientific methods in these studies. For the first time, evolutionary data have been summarized to describe both what evolution...