British flag theorem that and by a similar argument the squared lengths of the distances from "P" to the other three corners can be calculated as Therefore: This theorem takes its name from the fact that, when the line segments from "P" to the corners of the rectangle are drawn, together with the perpendicular lines used in the proof, the completed figure somewhat resembles a Union Flag. 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
Flag of the Natalia Republic 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 1840. British forces invaded the republic in May 1842, and