Began with a review of how to construct Voronoi cells as intersetions of half-spaces. Showed the following 3-dimensional Voronoi cell.
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<center><img src="uploads/voronoi.png" width=200 height=200></center>
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Described an algorithm, involving Voronoi cells, for finding the closest 
point in a finite set S to a vector v in <b>R</b><sup>n</sup>,  the finite set 
S being a collection (or database) of points in <b>R</b><sup>n</sup>.

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Stated the Johnson-Lindenstrauss Theorem and the Norm Preservation Proposition. Next lecture I'll explain how the latter implies the former, and that will complete Part I of the module.