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It is commonly believed in the literature that smooth curves, such as circles, are not fractal, and only non-smooth curves, such as coastlines, are fractal. However, this article demonstrates that a smooth curve can be fractal, under a new, relaxed, third definition of fractal – a set or pattern is fractal if the scaling of far more small things than large ones recurs at least twice. The scaling can be rephrased as a hierarchy, consisting of numerous smallest, a very few largest, and some in between the smallest and the largest. The logarithmic spiral, as a smooth curve, is apparently fractal because it bears the self-similarity property, or the scaling of far more small squares than large ones recurs multiple times, or the scaling of far more small bends than large ones recurs multiple times. A half-circle or half-ellipse and the UK coastline (before or after smooth processing) are fractal if the scaling of far more small bends than large ones recurs at least twice. [ABSTRACT FROM AUTHOR]