1 books for « hilbert david the ... »Edit

‎Ueber die stetige Abbildung einer Linie auf ein Flächenstück.‎

‎Leipzig, B.G. Teubner, 1891. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. Begründet durch Alfred Clebsch und Carl Neumann. 38. Band. 3. Heft."". (Entire issue offered). Pp. 315-460 a. 5 lithographed colourplates. Plates with a dampstain. The plates does not belong to Hilbert's paper). Hilbert's paper: pp. 459-460.‎

‎First appearace of Hilbert's importent papaer in which he introduces his space-filling curve or the Hilbert-Curve. He constructed an example of a curve that passed through every point of a square by a series of successive approximations. At each stage every square is divided into four equal smaller squares and the curve replaced.Although it was Peano [1890] that produced the first space-filling curves, it was Hilbert (in the paper offered) who first popularized their existence and gave an insight into their generation. Space-filling curves are commonly used to reduce a multidimensional problem to a one-dimensional problem" the curve is essentially a linear transversal of the discrete multidimensional space. ‎