haversinen.
/ˈhavəsʌɪn/, U.S. /ˈhævərˌsaɪn/ Mathematics.
A trigonometrical function given by haversin θ = ½(1 − cos θ), originally and chiefly used in navigational calculations; abbreviated haversin or hav. Frequently attributive.
ΚΠ
1835 J. Inman Navigation & Naut. Astron. (ed. 3) §307. 149 Add the halves of the log. haversine of the sum and difference.
1874 F. G. D. Bedford Sailor's Pocket Bk. ix. 294 Add together the log. secants of the two first terms..and the half haversines of the two last.
1922 J. A. Bullard & A. Kiernan Plane & Spherical Trigonom. 111 Haversine tables are being more and more widely used especially by the navigator.
1957 Amer. Math. Monthly 64 38 This formula is seldom derived. The derivation involves the rearrangement of the cosine formula for use with haversines.
2013 G. Van Brummelen Heavenly Math. ix. 160 A natural advantage of the haversine is that its values..are always positive.
Compounds
haversine formula n. a formula involving haversines which allows the shortest distance between two points on the surface of a sphere to be calculated using the longitude and latitude of each point.For two points on a sphere of radius r and having latitudes λ1, λ2 and longitudes ϕ1, ϕ2, the distance d between them is given by d = 2r arcsin (√h), where h = haversin (ϕ2 − ϕ1) + cos ϕ1 cos ϕ2 haversin (λ2 − λ1).
ΚΠ
1908 Math. Gaz. 4 269 The final reading for the angle A found by calculation above to illustrate the haversine formula to be 65°9′ coming out 65°30′.
1943 National Math. Mag. 17 327 In the first of the chapter the haversine formula is applied to the terrestrial triangle case of two sides and the included angle.
2009 Taxon 58 536/2 Geographic distances between populations were calculated using the ‘Haversine’ formula.
This entry has been updated (OED Third Edition, March 2015; most recently modified version published online March 2022).
<
n.1835