KOCH, Helge von.

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Sur une courbe continue sans tangente obtenue par une construction géométrique élémentaire. First edition, offprint issue, of one of the earliest mathematical constructions later recognized as a fractal: the Koch curve, or snowflake. The front wrapper has the ownership signature of the mathematician's sister, the artist Ebbe von Koch (1866-1943).Koch (1870-1924) described a curve that was continuous but not differentiable at any single point, thereby making it impossible to draw a tangent line. Although Karl Weierstrass had in 1872 demonstrated the existence of a similar function through purely analytic means, Koch was dissatisfied with the lack of a clear geometric representation and sought an explicit visual construction. When almost a century later Benoit Mandelbrot coined the term "fractal", Koch's curve was recognized as a canonical example of such self-similar, geometrically representable constructions. Applications of the Koch curve can be found in antenna engineering, heat transfer technology, and acoustics.

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