British Flag Theorem

In Euclidean geometry, the British flag theorem says that if a point P is chosen inside rectangle ABCD then the sum of the squared Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners. As an equation:

The theorem also applies to points outside the rectangle, and more generally to the distances from a point in Euclidean space to the corners of a rectangle embedded into the space. Even more generally, if the sums of squared distances from a point P to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference of the two sums will depend only on the shape of the parallelogram and not on the choice of P.

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Other articles related to "british flag theorem, theorem":

British Flag Theorem - Naming
... This theorem takes its name from the fact that, when the line segments from P to the corners of the rectangle are drawn, together with the perpendicular lines used in the proof, the ...

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