Gnomonic projections are used in seismic work because seismic waves tend to travel along great circles.

The gnomonic map projection displays great circles as straight lines. Image File history File links World map projection (source) File links The following pages link to this file: Map projection Gnomonic projection ... Jump to: navigation, search The Mercator projection shows courses of constant bearing as straight lines. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the...

Thus the shortest route between two locations in reality corresponds to that on the map. This is achieved by projecting, with respect to the center of the Earth (hence perpendicular to the surface), the Earth's surface onto a tangent plane. The least distortion occurs at the tangent point. Less than half of the sphere can be projected onto a finite map.

Since meridians and the Equator are great circles, they are always shown as straight lines.

• If the tangent point is one of the Poles then the meridians are radial and equally spaced. The equator is at infinity in all directions. Other parallels are depicted as concentric circles.

• If the tangent point is on the equator then the meridians are parallel but not equally spaced. The equator is a straight line perpendicular to the meridians. Other parallels are depicted as hyperbolae.

• In other cases the meridians are radially outward straight lines from a Pole, but not equally spaced. The equator is a straight line that is perpendicular to only one meridian (which again demonstrates that the projection is not conformal).

As for all azimuthal projections, angles from the tangent point are preserved. The map distance from that point is a function r(d) of the true distance d, given by Jump to: navigation, search Infinity is a term with very distinct, separate meanings which arise in theology, philosophy, mathematics and everyday life. ... Jump to: navigation, search In Euclidean geometry, a circle is the set of all points at a fixed distance, called the radius, from a fixed point, called the centre (center). ... A graph of a hyperbola, where h = k = 0 and a = b = 2. ... In mathematics, a conformal map is a function which preserves angles. ... The word projection can mean more than one thing. ...

r(d) = ctan(d/R)

where R is the radius of the Earth. The radial scale is

r′(d) = c/(2Rcos²(d/2R)

and the transverse scale

c/(2Rcos(d/2R)),

so the transverse scale increases outwardly, and the radial scale even more.

The gnomonic projection is said to be the oldest map projection, developed by Thales in the 6th century BC. Jump to: navigation, search Thales (in Greek: Θαλης) of Miletus (ca. ... (7th century BC - 6th century BCE - 5th century BCE - other centuries) (600s BCE - 590s BCE - 580s BCE - 570s BCE - 560s BCE - 550s BCE - 540s BCE - 530s BCE - 520s BCE - 510s BCE - 500s BCE - other decades) (2nd millennium BCE - 1st millennium BCE - 1st millennium) The 5th and 6th centuries BCE were...

External links

• http://www.3dsoftware.com/Cartography/USGS/MapProjections/Azimuthal/Gnomonic/
• http://exchange.manifold.net/manifold/manuals/6_userman/mfd50Gnomonic.htm
• http://mathworld.wolfram.com/GnomonicProjection.html
• http://members.shaw.ca/quadibloc/maps/maz0201.htm

References

Snyder, John P. (1987) Map Projections - A Working Manual. U.S. Geological Survey Professional Paper 1395, United States Government Printing Office, Washington, D.C.. This paper can be dowloaded from USGS pages