### DIMACS Special Theoretical Computer Science Seminar

Title: The Expansion Coefficient of the Peano-Hilbert Curve

Speaker: **Konstantin Bauman**

Date: Friday, February 9, 2007 11:00-12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Peano curve is used at coding information, numerical integration and in other mathematical applications. The quadric-linear ratio is defined as a maximum relation of a square of distance between images of points and distance between these points. It's a very important characteristic of Peano curve. For applications the best curve is that curve which has the least quadric-linear ratio.

We can count the quadric-linear ratio for any Peano curve with the given accuracy by computer. But it is a very interesting problem in fractal geometry to find the extract value of quadric-linear ratio. I have proved the first result of this sort. According to my work, the maximal quadric-linear ratio for the classical Peano-Hilbert curve is equal to six. This result is very useful for applications.