This article is cited in 39 papers

The dilation factor of the Peano–Hilbert curve

K. E. Bauman

M. V. Lomonosov Moscow State University

Abstract: It is proved that the maximum value of the ratio $|p(x)-p(y)|^2/|x-y|$ for the Peano–Hilbert curve $p\colon[0,1]=I\to I^2$ is equal to 6.

UDC: 514.8

Received: 03.04.2006

DOI: 10.4213/mzm3074

 English version: Mathematical Notes, 2006, 80:5, 609–620

Bibliographic databases:

• 
• 
• 
• 
•