Many people, when they look back, can pinpoint the precise moment when their interest in mathematics was awakened - it was when they found a puzzle that intrigued them. Perhaps they now realise the puzzle was trivial or insignificant, but at the time something about it captured their imagination and started them on a path that may have led very far - perhaps even into fundamental mathematical research.
This video, aimed at students aged 16+, opens with Professor Chris Budd holding the plastic yellow duck he is entering in the Annual Bath Plastic Duck Race. Competition is stiff - there are over 3,000 contestants - but how can we predict who will win? Very few competitors have form, and it's hard to tell much about their training regimens... so is the outcome totally unpredictable?
Ballet and mathematics - not a combination that you often come across, but one that works beautifully in Frederick Ashton's 1948 ballet, Scénes de ballet. From the geometric patterns on the men's tunics and the perpendicular angle of the ballerina's tutu, to the movements and positioning of the dancers themselves, this ballet is a celebration of mathematics. Ashton was inspired by mathematics, and, according to the programme notes, used a system of Euclidean geometry to choreograph the piece.
Not many books about maths have chapters that start "The dead man seemed to stare at me in a most disconcerting way." But maybe more should - this book is a highly entertaining read, crossing sound mathematical exposition with the classic Sherlock Holmes style of investigation.
Many popular books about mathematics combine elements of exposition and personal commentary, but few combine these disparate elements to the same extent as this book.

Since the phenomenal success of "The little book of calm", publishers have been falling over themselves to produce "little books" of everything else, presumably in the hope that the essential ingredient was the littleness, rather than the calmness. Although, at 5 inches by 7¼, "1089 and all that" makes a rather big little book, and its content couldn't be further from the banalities of "The little book of calm", there is something of a "little book of mathematics" about it, with its short chapters and personal narrative.