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:
“About the alleged condition of the property. Does it have to be intact?”
—Margaret Forster, British screenwriter, Peter Nichols, and Silvio Narizzano. Georgy (Lynn Redgrave)
“My dream is that as the years go by and the world knows more and more of America, it ... will turn to America for those moral inspirations that lie at the basis of all freedom ... that America will come into the full light of the day when all shall know that she puts human rights above all other rights, and that her flag is the flag not only of America but of humanity.”
—Woodrow Wilson (1856–1924)
“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)