Symmetry. Transl. from the original German by Peter Hilton, with the assistance of Jean Pedersen (Q2715699)

[For a review of the German original (Teuber 1998) see Zbl 0890.00003).] NEWLINENEWLINENEWLINEThis about 100-page book includes chapters on reflection in a mirror, reflection in a circle, symmetric procedure (i.e., a few pages on symmetry as a method), tiling and lattices, idea of a center, and palindromes. Surely, this material is interesting and could serve as a background for a presentation of ideas on many levels. NEWLINENEWLINENEWLINEAccording to the author, ``this book is directed towards students, schoolgirls and schoolboys, as well as their teachers and interested laymen''. Yet, the book is built on posing ambiguous questions, and later giving ambiguous answers. One wonders what can schoolgirls and schoolboys possibly understand and gain here. For example, right on page 7 of the book the author asks the readers to calculate the area of a fractal (Sierpinski triangle). Two pages later, in his ``answer'' the author computes this area by adding an infinite series with no definition of what a sum of infinitely many summands can possibly mean, and without addressing the existence. The author asks to compute the length of a diagonal that consists of infinitely many segments without defining what ``length'' could mean in such a context (p. 7). Young American readers are not familiar with vectors, which the author starts using on page 31, thus, the translator should have added the necessary definitions and introduction. But surely neither American nor Swiss schoolgirls know double integral that suddenly appears in a formula on page 32, and according to the author actually ``leads us [i.e., readers] to the same formula\dots''. Thus, in the opinion of this reviewer, the intended audience of this book would primarily gain a great deal of confusion\dots NEWLINENEWLINENEWLINE``When I saw the original German text of Symmetry, by Hans Walser, I was immediately impressed by the stimulating nature of its contents -- and warmly recommended to the MAA that they publish a translation'' -- writes Peter Hilton, who also translated the book. Perhaps, MAA and Professor Hilton would enlighten us as to how this booklet could stimulate youthful readers who do not know the subject, and how it could be valued by older readers who do.