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 first table of haversines in english was published by james andrew in 1805.heavenly mathematics: the forgotten art of spherical trigonometry by glen van brummelen florian cajori credits an earlier use by jose de mendoza y rÃ­os in 1801a history of mathematical notations: vol. ii by florian cajori the term haversine was coined in 1835 by prof. james inman.oxford english dictionary. oxford university press. 2nd ed. 1989. cites coinage of term "haversine" by prof. jas. inman, d. d., in his navigation and nautical astronomy, 3rd ed. (1835). these names follow from the fact that they are customarily written in terms of the haversine function, given by haversin(Î¸) = sin2(Î¸/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, the elimination of division and multiplication by factors of two proved convenient enough that tables of haversine values and logarithms were included in 19th and early 20th century navigation and trigonometric texts.h. b. goodwin, the haversine in nautical astronomy, naval institute proceedings, vol. 36, no. 3 (1910), pp. 735â746: evidently if a table of haversines is employed we shall be saved in the first instance the trouble of dividing the sum of the logarithms by two, and in the second place of multiplying the angle taken from the tables by the same number. this is the special advantage of the form of table first introduced by professor inman, of the portsmouth royal navy college, nearly a century ago.w. w. sheppard and c. c. soule, practical navigation (world technical institute: jersey city, 1922).e. r. hedrick, logarithmic and trigonometric tables (macmillan, new york, 1913). these days, the haversine form is also convenient in that it has no coefficient in front of the sin2 function. ==the haversine formula== for any two points on a sphere, the haversine of the central angle between them is given by :\operatorname{haversin}\left(\frac{d}{r}\right) = \operatorname{haversin}(\phi_2 - \phi_1) + \cos(\phi_1) \cos(\phi_2)\operatorname{haversin}(\lambda_2-\lambda_1) where * haversin is the haversine function: :\operatorname{haversin}(\theta)=\sin^2\left(\frac{\theta}{2}\right)=\frac{1-\cos(\theta)}{2} * d is the distance between the two points (along a great circle of the sphere; see [[great-circle distance|spher
Geolocation Spherical_trigonometry