This work studies the Zipf law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in Brazilian cities does follow a power-law similar to the ones found in other countries. Estimates of the power-law exponent were found to be 2.22+/-0.34 for the 1970 and 1980 censuses, and 2.26+/-0.11 for censuses of 1991 and 2000. More accurate results were obtained with the maximum likelihood estimator, showing an exponent equal to 2.41 for 1970 and 2.36 for the other 3 years.

We present a broad, phenomenological picture of the distribution of the length of open space linear segments, l, derived from maps of 36 cities in 14 different countries. By scaling the Zipf plot of l, we obtain two master curves for a sample of cities, which are not a function of city size. We show that a third class of cities is not easily classifiable into these two universality classes. The cumulative distribution of l displays power-law tails with two distinct exponents, [alpha]B=2 and [alpha]R=3. We suggest a link between our data and the possibility of observing and modelling urban geometric structures using Levy processes.