The arc is [i]oriented.[/i] It respects the equivalence of these three statements:[br][math]\;\;\;[/math] Arc BC subtends central angle BAC,[br][math]\;\;\;[/math] There is a one-to-one correspondence between points on arc BC and points on segment BC.[br][math]\;\;\;[/math] The arc respects minimum rotation.[br][br]We may then preserve measure:[br]|BC| (magnitude) is the distance from B to C (direction).[br]|∡BAC| (magnitude) is the angle from B to C (direction/sign).