Symmetry abounds: the wallpaper, your chair, even your own body. Familiar types of symmetry include reflection in a line and rotation about a point. Creating a repeating pattern by translating a core segment to a new place, common in wallpaper, also counts as a symmetry, as does switching without the use of a mirror from an anticlockwise segment to one otherwise identical but oriented clockwise.
I would guess that, even a decade ago, the phrase "mathematical recreation" would have been considered a contradiction in terms. Now, in the age of compulsive Sudoku puzzlers, and an increasing canon of popular mathematics books, this descriptor has become credible.
"Oh god, I hope not," was the reaction of a student when Livio asked the title question at a lecture, and it's a reaction that's likely to be replicated by many unsuspecting bookshop browsers. But despite its frightening title, the book's appeal could not be broader.