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.

Read more about British Flag Theorem:  Proof, Naming

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    It’s simple: either you have discipline or you haven’t.
    Edmund H. North, British screenwriter, and Lewis Gilbert. Captain Shepard (Kenneth More)

    Hath not the morning dawned with added light?
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    To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
    Albert Camus (1913–1960)