Alan Davies sets out to answer a question that sounds like a joke and turns out to be a real mathematical puzzle: how do you measure something whose length keeps changing depending on how closely you look? He visits mathematician Marcus du Sautoy, who walks him through the coastline paradox, the discovery that measuring Britain's coast with a shorter and shorter ruler produces a longer and longer number, with no clear end point. From there the film moves into fractals and the strange geometry of shapes that are rough at every scale, using string, coastlines, and everyday objects to make abstract ideas physical. Davies plays the curious non-mathematician throughout, asking the questions a viewer would ask, while du Sautoy supplies the proofs and the history behind them. The film treats a seemingly trivial question as a route into infinity, dimension, and the limits of measurement itself, and it stays grounded in demonstrations rather than abstraction.