Peano curve (nonfiction)

Three iterations of the Peano curve.

In geometry (nonfiction), the Peano curve, discovered by Giuseppe Peano (nonfiction) in 1890, is the earliest known space-filling curve.

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 (nonfiction) 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.

Fiction cross-reference

• Georg Cantor (nonfiction)
• Giuseppe Peano (nonfiction)

Nonfiction cross-reference

• Giuseppe Peano (nonfiction)
• Hilbert curve (nonfiction)

External links:

• Peano curve @ Wikipedia
• Space-filling curve @ Wikipedia