Abstrakt
In this contribution, we present the concept of the Peano curve, i.e. the space-filling curve that goes through each point of a square. We first present two algorithms for its construction which are also used in teaching programming at universities as an exercise in recursion: Peano's original algorithm in its more intuitive form and the subsequent interpretation given by D.
Hilbert. Then we discuss some mathematical properties of the curve.
We take advantage of the history of mathematics (2nd half of the 19th century) and quote Hilbert's correspondence with H. Minkowski on this topic.
We present Cantor's previous non-continuous mappings on a couple of intuitive examples. This way, we explain the Peano curve in context with set theory.
Finally, we briefly mention contemporary applications of the curve in computer science.