HILBERT, DAVID. - THE HILBERT SPACE-FILLING CURVE.

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.

Order-nr.: 45869