Mathematics in Berlin Book

This is a wonderful book, beautifully produced,illustrated and edited, and, considering its subject-matter, requiring amazingly little in the way of previous mathematical knowledge. It will be most enjoyed by readers prepared to undertake the "projects" that occur through-out the book, which means that access to a computer, and some means of programming will be needed. However, it is beautiful just to look at, and has many short standalone sections (such as potted histories and biographies), which make this an excellent book for a mathematician to have on his or her coffee table. A teacher running a maths-club or a computer-programming club for bright secondary school students ought to be able to find plenty of interesting projects in this book.

Early chapters of the book explain the concepts of symmetry groups, complex numbers, and transformations. Then the reader is introduced to Möbius transformations and various families of Kleinian groups with each new family giving rise to more intricate fractal patterns than the last, and by the end of the book has learned some of the mysteries of cusp and degenerate groups, and the connections with hyperbolic geometry.

I cannot commend this book too highly. Even casual readers can enjoy dipping into it, or simply enjoy the pictures, but it is a book to be studied and worked at over a long period. 7 years after buying it there are still ideas within it that I am still exploring and learning more about.