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.
Famous quotes containing the words british, flag and/or theorem:
“In New York—whose subway trains in particular have been “tattooed” with a brio and an energy to put our own rude practitioners to shame—not an inch of free space is spared except that of advertisements.... Even the most chronically dispossessed appear prepared to endorse the legitimacy of the “haves.””
—Gilbert Adair, British author, critic. “Cleaning and Cleansing,” Myths and Memories (1986)
““Justice” was done, and the President of the Immortals, in Æschylean phrase, had ended his sport with Tess. And the d’Urberville knights and dames slept on in their tombs unknowing. The two speechless gazers bent themselves down to the earth, as if in prayer, and remained thus a long time, absolutely motionless: the flag continued to wave silently. As soon as they had strength they arose, joined hands again, and went on.
The End”
—Thomas Hardy (1840–1928)
“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)