Sketchpad Resources || Main CIGS Page Dirichlet Regions for
Three Points: The loci of circle intersections trace the
boundaries of three Dirichlet regions, each containing one of
the points A, B, C. The Dirichlet region containing A, for
example, is the set of points P which are closer to A than to
any of the other points B or C. It follows that the boundary
between two Dirichlet regions is the set where distances to two
of the points A, B, C are equal and less than the third
distance. Finally, the corner or vertex is the point where the 3
distances to A, B, and C are equal. We recognize this as the
circumcenter of triangle ABC. Since the circles have the same
radius. The points on the circles have the same distances to the
corresponding centers, so the intersection points of two circles
are equidistant from two of the three points A, B, C. Dirichlet
Regions for Four Points Dirichlet Regions for Five Points Home
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