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Social scientists have developed dozens of different ways to quantify urban segregation with numerical statistics. Behind the scenes, some of these measurements are defined using multivariable functions that model the distribution of various groups in a geographical region. Using Bayes' theorem and kernel density estimation, we describe how to summarize population data in terms of smooth, two-dimensional surfaces. These surfaces give us ways of identifying neighborhood boundaries and visualizing segregation patterns. We also propose two new segregation measures using some familiar tools from third-semester calculus. Applications to United States census data are included. [ABSTRACT FROM AUTHOR]