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The study of convergence usually deals with perspective, or series. Most literally, our eyes will each see a separate image, and our brains can make the images converge so that we'll see a single object. In triangles, whether a certain set of lines will meet at a single point is known as a concurrence problem. One example of three concurrent points is given by the Fermat point, illustrated below. This is just one of many triangle centers.
FermatPoint
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