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Peano surface

Model of the Peano surface in the Dresden collection

In mathematics, the Peano surface is the graph of the two-variable function

It was proposed by Giuseppe Peano in 1899 as a counterexample to a conjectured criterion for the existence of maxima and minima of functions of two variables.[1][2]

The surface was named the Peano surface (German: Peanosche Fläche) by Georg Scheffers in his 1920 book Lehrbuch der darstellenden Geometrie.[1][3] It has also been called the Peano saddle.[4][5]

  1. ^ a b Emch, Arnold (1922). "A model for the Peano Surface". American Mathematical Monthly. 29 (10): 388–391. doi:10.1080/00029890.1922.11986180. JSTOR 2299024. MR 1520111.
  2. ^ Genocchi, Angelo (1899). Peano, Giuseppe (ed.). Differentialrechnung und Grundzüge der Integralrechnung (in German). B.G. Teubner. p. 332.
  3. ^ Scheffers, Georg (1920). "427. Die Peanosche Fläche". Lehrbuch der darstellenden Geometrie (in German). Vol. II. pp. 261–263.
  4. ^ Krivoshapko, S. N.; Ivanov, V. N. (2015). "Saddle Surfaces". Encyclopedia of Analytical Surfaces. Springer. pp. 561–565. doi:10.1007/978-3-319-11773-7_33. See especially section "Peano Saddle", pp. 562–563.
  5. ^ Francis, George K. (1987). A Topological Picturebook. Springer-Verlag, New York. p. 88. ISBN 0-387-96426-6. MR 0880519.

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