British flag theorem 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
Flag of the Natalia Republic Rijksarchief in the Netherlands in 1953, shows a square flag. Flag of the Natalia Republic The flag of the Natalia Republic was the official flag of this short lived South African state, which existed from 1839 to 1843. Emigrant Boers ('voortrekkers') from the Cape Colony established an independent state in 1839, on territory conquered from the Zulus. They named it 'Natalia'. It is uncertain what flag – if any – they flew at first, but on 24 December 1839 they raised a new flag at Port Natal (now Durban. The same flag was raised in the capital, Pietermaritzburg, in January