Binary scaling always a valid angle in the range of −180° degrees (−π radians) to +180° degrees (+π radians). In some cases, it is convenient to use unsigned multiplication (rather than signed multiplication) on a binary angle, which gives the correct angle in the range of 0 to +360° degrees (+2π radians or +1 turn). Compared to storing angles in a binary angle format, storing angles in any other format inevitably results in some bit patterns giving "angles" outside that range, requiring extra steps to range-reduce the value to the desired range, or results in some bit patterns that are not valid
Space (mathematics) projective geometry nor defined from the notions mentioned there. The question "what is the sum of the three angles of a triangle" is meaningful in Euclidean geometry but meaningless in projective geometry. A different situation appeared in the 19th century: in some geometries the sum of the three angles of a triangle is well-defined but different from the classical value (180 degrees). Non-Euclidean hyperbolic geometry, introduced by Nikolai Lobachevsky in 1829 and János Bolyai in 1832 (and Carl Friedrich Gauss in 1816, unpublished) stated that the sum depends on the triangle and is always less than 180 degrees. Eugenio Beltrami