Back منحنى بيانو Arabic Corba de Peano Catalan Peanova křivka Czech Peano-Kurve German Καμπύλη Πεάνο Greek Curva de Peano Spanish خم پئانو Persian Courbe de Peano French עקום פאנו HE Curva di Peano Italian
Two iterations of a Peano curve
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890.[1] Peano's curve is a surjective, continuous function from the unit interval onto the unit square, however it is not injective. Peano was motivated by an earlier result of Georg Cantor that these two sets have the same cardinality. Because of this example, some authors use the phrase "Peano curve" to refer more generally to any space-filling curve.[2]
- ^ Peano, G. (1890), "Sur une courbe, qui remplit toute une aire plane", Mathematische Annalen, 36 (1): 157–160, doi:10.1007/BF01199438.
- ^ Gugenheimer, Heinrich Walter (1963), Differential Geometry, Courier Dover Publications, p. 3, ISBN 9780486157207.