Definition:Haversine

Definition

The haversine of an angle is defined as:

$\ds \hav \theta$

$=$

$\ds \dfrac 1 2 \paren {1 - \cos \theta}$

$\ds $

$=$

$\ds \dfrac 1 2 \vers \theta$

where $\vers \theta$ denotes the versed sine of $\theta$

$\ds $

$=$

$\ds \sin^2 \dfrac {\theta} 2$

In the days before digital computers, log tables and slide rules were de rigueur in all fields of mathematics where calculation was involved.

Calculation of distances and directions on the surface of Earth using the Spherical Law of Cosines and its derived formulas is computation-intensive.

The Spherical Law of Haversines is easier to use, assuming one has a table of haversines and logarithms of haversines.

Hence use of the haversine was commonplace in nautical context.

The word haversine derives from half versed sine.