There are various problems one can have with shoelaces (broken shoelaces, undone shoelaces, missing shoelaces, too long or too short shoelaces and so on). Mathematically minded people however might find interest in yet another set of problems, very different from those mentioned. These include questions like: ‘What is the shortest/longest/strongest/weakest way to lace the shoes?’ and ‘How many ways are there to lace the shoes?’. This beautiful and amusing book attacks all these problems from a mathematical point of view. It all started with an innocent article published by the author in 2002 in the journal Nature, which attracted an enormous amount of publicity and great interest in the mathematics of shoelaces from many people in all walks of life. The mathematics of shoelaces is a lovely combination of combinatorics and elementary analysis. It has nice and surprising connections to things like the travelling salesman problem or calculating the area of simply closed planar polygons. The book also has sections on the history of shoelacing, shoelace superstitions, style and fashion, and at the end it tackles the difficult philosophical question: what is the best way to lace the shoes? A very enjoyable book indeed.

Reviewer:

lp