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Holmes and Watson were sitting quietly, awaiting the arrival of the guest for the New Year's Eve dinner Holmes had arranged. "In fact, Watson,", Holmes observed, "even more elementarily than your parabola, the circle with centre the point R of intersection of line V and the segment S extended and passing through the optimal vantage point has radius given by the same formula in T and S, provided T is interpreted as the distance from R to the segment S. This can be shown by using Pythagoras's Theorem twice." At that moment the door chime sounded. "That must be Miss Adler. I look forward to her telling us the latest from Paris and her discussions with Poincare. You may not be aware that she and he were both students at the same time of Hermite."

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