Haversine formula

The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical triangles. The term haversine was coined in 1835 by Prof. James Inman

These names follow from the fact that they are customarily written in terms of the haversine function, given by haversin(θ) = sin2(θ/2). The formulas could equally be written in terms of any multiple of the haversine, such as the older versine function (twice the haversine). Prior to the advent of computers, theelimination of division and multiplication by factors of two provedconvenient enough that tables of haversine values and logarithms were included in 19th and early 20th century navigation and trigonometric texts. These days, the haversine form is also convenient in that it has no coefficient in front of the sin2 function.