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:
“You British plundered half the world for your own profit. Let’s not pass it off as the Age of Enlightenment.”
—Paddy Chayefsky (1923–1981)
“—Here, the flag snaps in the glare and silence
Of the unbroken ice. I stand here,
The dogs bark, my beard is black, and I stare
At the North Pole. . .
And now what? Why, go back.
Turn as I please, my step is to the south.”
—Randall Jarrell (1914–1965)
“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)