Circle of latitude can be calculated by a common sine or cosine function. The 60th parallel north or south is half as long as the Equator (disregarding Earth's minor flattening by 0.3%). A circle of latitude is perpendicular to all meridians. The latitude of the circle is approximately the angle between the Equator and the circle, with the angle's vertex at Earth's centre. The equator is at 0°, and the North Pole and South Pole are at 90° north and 90° south, respectively. The Equator is the longest circle of latitude and is the only circle of latitude which also is a great
Rhumb line ship's latitude could be established accurately by sightings of the Sun or stars but there was no accurate way to determine the longitude. The ship would sail north or south until the latitude of the destination was reached, and the ship would then sail east or west along the rhumb line (actually a parallel, which is a special case of the rhumb line), maintaining a constant latitude and recording regular estimates of the distance sailed until evidence of land was sighted. The surface of the Earth can be understood mathematically as a Riemann sphere, that is, as a projection of