haversine

I see everything but how you hide haversine tables in a jump suit.

There are several related functions, most notably the coversine and haversine.

Note that the argument to the haversine function is assumed here to be given in radians.

This computation of the altitude and the azimuth needs a haversine table.

Since the haversine formula uses sines it avoids that problem.

The latter, half a versine, is of particular importance in the haversine formula of navigation.

With this information it is possible using the haversine formula to calculate the latitude where the position line crosses the assumed longitude.

The haversine formula is numerically better-conditioned for small distances:

(For details of the calculation, see Haversine formula.)

Knowledge (without proof) of the spherical haversine formula and its use in solving oblique spherical triangles.

The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.

In situations where this is an important concern, a mathematically equivalent version of the law of cosines, similar to the Haversine formula, can prove useful:

The formulas could equally be written in terms of any multiple of the haversine, such as the older versine function (twice the haversine).

So I treated H-above-G, ten klicks, as a versine, applied the haversine rule and got four degrees thirty-seven minutes or two hundred seventy-seven kilometers to the theoretical horizon.

As sagitta and cosagitta, double-angle Δ variants of the haversine and havercosine have also found new uses in describing the correlation and anti-correlation of correlated photons in quantum mechanics.

Instead, an equation known historically as the haversine formula was preferred, which is much more accurate for small distances:R.W. Sinnott, "Virtues of the Haversine", Sky and Telescope, vol.

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.

In the form of sin(θ) the haversine of the double-angle Δ describes the relation between spreads and angles in rational trigonometry, a proposed reformulation of metrical planar and solid geometries by Norman John Wildberger since 2005.

Thirdly, since a geohash (in this implementation) is based on coordinates of longitude and latitude the distance between two geohashes reflects the distance in latitude/longitude coordinates between two points, which does not translate to actual distance, see Haversine formula.

The haversine continues to be used in navigation and has even found new applications in recent decades, like in Bruce D. Stark's method for clearing lunar distances utilizing Gaussian logarithms since 1995 or in a more compact method for sight reduction since 2014.

The haversine, in particular, was important in navigation because it appears in the haversine formula, which is used to accurately compute distances within reason on an astronomic spheroid (see issues with the earth's radius vs. sphere) given angular positions (e.g., longitude and latitude).

Spherical trigonometry used to be an important mathematics topic from antiquity through the end of World War II, and has been replaced in modern education and (in navigation) with more algorithmic methods as well as GPS, including the Haversine formula, linear algebraic matrix multiplication, and Napier's pentagon.