LiveMath - Revision history

en>ScotXW: added Category:Proprietary commercial software for Linux using HotCat

2014-04-07T15:40:23Z

added Category:Proprietary commercial software for Linux using HotCat

← Older revision		Revision as of 17:40, 7 April 2014
Line 1:		Line 1:
	~~[[File:Van der Grinten projection SW~~.~~jpg\|250px\|thumb\|Van der Grinten projection of the world~~.]]		I would like to introduce myself to you, I am Jayson Simcox but I don't like when individuals use my full title. Distributing manufacturing has been his profession for some time. To play lacross is the factor I adore most of all. I've always cherished living in Mississippi.<br><br>Stop by my website - [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 psychic solutions by lynne]
	~~The '''van der Grinten projection'''~~ is ~~a compromise [[map projection]] that is neither [[Map projection#Equal-area\|equal-area]] nor [[conformal map projection\|conformal]]. It projects~~ the ~~entire Earth into a circle, though the polar regions are subject to extreme distortion. The projection was the first~~ of ~~four proposed by Alphons J~~. ~~van der Grinten~~ in 1904, and, unlike most projections, is an arbitrary geometric construction on the plane. It was made famous when the [[National Geographic Society]] adopted it as their reference map of the world from 1922 until 1988.<~~ref~~>~~''Flattening the Earth: Two Thousand Years of Map Projections'', John P. Snyder, 1993, pp.258-262, ISBN 0-226-76747-7.~~<~~/ref~~>

	~~The geometric construction given~~ by ~~van der Grinten can be written algebraically:<ref>~~[http://~~pubs.er.usgs~~.~~gov/usgspubs/pp/pp1395 ''Map Projections~~ - ~~A Working Manual''], [[United States Geological Survey\|USGS]] Professional Paper 1395, John P. Snyder, 1987, pp.239~~-~~242</ref>~~

	~~:<math>x = \frac {\pm \pi \left(A\left(G - P^2\right) + \sqrt {A^2 \left(G - P^2\right)^2 - \left(P^2 + A^2\right)\left(G^2 - P^2\right)}\right)} {P^2 + A^2}\,</math>~~

	~~:<math>y = \frac {\pm \pi \left(P Q - A \sqrt{\left(A^2 + 1\right)\left(P^2 + A^2\right) - Q^2} \right)} {P^2 + A^2}</math>~~

	~~where <math>x\,</math> takes the sign of <math>\lambda - \lambda_0\,</math>, <math>y\,</math> takes the sign of <math>\phi\,</math> and~~

	~~:<math>A = \frac {1} {2}\|\frac {\pi} {\lambda - \lambda_0} - \frac {\lambda - \lambda_0} {\pi}\|</math>~~
	~~:<math>G = \frac {\cos \theta} {\sin \theta + \cos \theta - 1}</math>~~
	~~:<math>P = G\left(\frac {2} {\sin \theta} - 1\right)</math>~~
	~~:<math>\theta = \arcsin \|\frac {2 \phi} {\pi}\|</math>~~
	~~:<math>Q = A^2 + G\,</math>~~

	~~Should it occur that <math>\phi = 0\,</math>, then~~

	~~:<math>x = \left(\lambda - \lambda_0\right)\,</math>~~
	~~:<math>y = 0\,</math>~~

	~~Similarly, if <math>\lambda = \lambda_0\,</math> or <math>\phi = \pm \pi / 2\,</math>, then~~

	~~:<math>x = 0\,</math>~~
	~~:<math>y = \pm \pi \tan {\theta / 2 }</math>~~

	~~In all cases, <math>\phi\,</math> is the latitude, <math>\lambda\,</math> is the longitude, and <math>\lambda_0\,</math> is the central meridian of the projection.~~

	~~==See also==~~
	~~{{Portal\|Atlas}}~~
	* [[List of map projections]]

	~~==References==~~
	~~{{reflist}}~~

	~~=== Sources ===~~
	* {{cite web\|url=http://www.progonos.com/~~furuti/MapProj/Normal/ProjOth/projOth~~.~~html\|title~~=~~Projections~~ by ~~Van der Grinten, and variations}}~~

	~~{{Map Projections}}~~

	~~[[Category:Cartographic projections~~]]

	~~{{cartography-stub}}~~

en>Glenn: catchg

2014-01-01T11:20:47Z

catchg

← Older revision		Revision as of 13:20, 1 January 2014
Line 1:		Line 1:
	~~Andrew Berryhill~~ is ~~what his wife enjoys to call him and he completely digs~~ that ~~name~~. ~~Her family members lives in Ohio but her husband desires them~~ to ~~move~~. ~~Office supervising~~ is ~~my occupation~~. ~~What I adore performing is football but I don~~'~~t have~~ the ~~time lately~~.<br><br>~~Stop by my site;~~ [http://www.~~article-galaxy~~.com/~~profile~~.~~php?a~~=~~143251 psychic love readings~~]		[[File:Van der Grinten projection SW.jpg\|250px\|thumb\|Van der Grinten projection of the world.]]
			The '''van der Grinten projection''' is a compromise [[map projection]] that is neither [[Map projection#Equal-area\|equal-area]] nor [[conformal map projection\|conformal]]. It projects the entire Earth into a circle, though the polar regions are subject to extreme distortion. The projection was the first of four proposed by Alphons J. van der Grinten in 1904, and, unlike most projections, is an arbitrary geometric construction on the plane. It was made famous when the [[National Geographic Society]] adopted it as their reference map of the world from 1922 until 1988.<ref>''Flattening the Earth: Two Thousand Years of Map Projections'', John P. Snyder, 1993, pp.258-262, ISBN 0-226-76747-7.</ref>

			The geometric construction given by van der Grinten can be written algebraically:<ref>[http://pubs.er.usgs.gov/usgspubs/pp/pp1395 ''Map Projections - A Working Manual''], [[United States Geological Survey\|USGS]] Professional Paper 1395, John P. Snyder, 1987, pp.239-242</ref>

			:<math>x = \frac {\pm \pi \left(A\left(G - P^2\right) + \sqrt {A^2 \left(G - P^2\right)^2 - \left(P^2 + A^2\right)\left(G^2 - P^2\right)}\right)} {P^2 + A^2}\,</math>

			:<math>y = \frac {\pm \pi \left(P Q - A \sqrt{\left(A^2 + 1\right)\left(P^2 + A^2\right) - Q^2} \right)} {P^2 + A^2}</math>

			where <math>x\,</math> takes the sign of <math>\lambda - \lambda_0\,</math>, <math>y\,</math> takes the sign of <math>\phi\,</math> and

			:<math>A = \frac {1} {2}\|\frac {\pi} {\lambda - \lambda_0} - \frac {\lambda - \lambda_0} {\pi}\|</math>
			:<math>G = \frac {\cos \theta} {\sin \theta + \cos \theta - 1}</math>
			:<math>P = G\left(\frac {2} {\sin \theta} - 1\right)</math>
			:<math>\theta = \arcsin \|\frac {2 \phi} {\pi}\|</math>
			:<math>Q = A^2 + G\,</math>

			Should it occur that <math>\phi = 0\,</math>, then

			:<math>x = \left(\lambda - \lambda_0\right)\,</math>
			:<math>y = 0\,</math>

			Similarly, if <math>\lambda = \lambda_0\,</math> or <math>\phi = \pm \pi / 2\,</math>, then

			:<math>x = 0\,</math>
			:<math>y = \pm \pi \tan {\theta / 2 }</math>

			In all cases, <math>\phi\,</math> is the latitude, <math>\lambda\,</math> is the longitude, and <math>\lambda_0\,</math> is the central meridian of the projection.

			==See also==
			{{Portal\|Atlas}}
			* [[List of map projections]]

			==References==
			{{reflist}}

			=== Sources ===
			* {{cite web\|url=http://www.progonos.com/furuti/MapProj/Normal/ProjOth/projOth.html\|title=Projections by Van der Grinten, and variations}}

			{{Map Projections}}

			[[Category:Cartographic projections]]

			{{cartography-stub}}

en>Gesslein: use URL template for website address

2011-10-01T01:00:35Z

use URL template for website address

New page

Andrew Berryhill is what his wife enjoys to call him and he completely digs that name. Her family members lives in Ohio but her husband desires them to move. Office supervising is my occupation. What I adore performing is football but I don't have the time lately.<br><br>Stop by my site; [http://www.article-galaxy.com/profile.php?a=143251 psychic love readings]