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| [[File:Cylindrical equal-area projection SW.jpg|400px|thumb|Cylindrical equal-area projection of the world; standard parallel at 40°N.]]
| | This should be followed by a thorough check over for damage. Make a conscious effort to check out tire tread performance under various conditions. The trail then follows the side of the glacial Lake Pukaki through to Twizel, the town build in the 60s only to house workers from the Waitaki Hydroelectricity Scheme. If the skin diameter is smaller than a quarter do not be surprised if you must change them a couple of instances per season to keep the bike working reliably. If you have any queries with regards to where and how to use [http://fungonline.com/profile/124586/jumaestas Biking for modern life mountain bike sizing.], you can get hold of us at the internet site. Two hunters may choose to use trailers if their distance from the truck is over four or five miles. <br><br>There are also single speed mountain bikes that only have one set gear ratio. After their devastating loss to the Dallas Mavericks, there has been a lot of question as to whether they are really capable of winning a title or not. David Moffat founded Winter Park as a workers camp during construction of the Moffat Tunnel while building the transcontinental railroad from Denver to the Pacific. Cost shouldn't be a factor as a good helmet can be acquired for around $25-$45. Full suspensions are of course the most comfortable. <br><br>Technological know-how is advancing very rapidly and manufactures have observed ways to make batteries much more efficient and Eco-pleasant at the very same time along with photo voltaic PV cells getting additional and a lot more effortless and economical to make. Here are some of the more popular mountain bike wheels now available [*CO]. The tape (or string against the ruler) will indicate what your helmet size is. Follow these simple tips and maximize your riding time while you wait for the snow to fall again. The suitable quill stems are sized down to the internal diameter of your fork's steer tube. <br><br>When discount sales are on, you need to be sure you understand the terms and conditions of your purchase, including warranty information. You can surpass your rivals if you participate in a match. In the purest sense of the word, a mountain bikes sole mission is to travel "off-road" only. Now do your comparison-shopping based on five or six available bikes. To help you choose which one you to buy, here are the list of bikes and their use. <br><br>I ran with Hale and we also tried this method, it was effective. They get used on the street which is not what it's built for. Are you going to be going up and down hills, across flat terrain, on cement, or through rough and rocky areas. Hence, XC suspension forks tend to have a short travel and are light weight. They will provide you with a honest price, yet be ready to pay in between $650 and $4,000 on dual suspensions and in between $470 and $670 for hardtails. |
| [[Image:Tissot indicatrix world map Lambert cyl equal-area proj.svg|400px|thumb|The Lambert cylindrical equal-area projection with [[Tissot's indicatrix]] of deformation]]
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| [[File:Cylindrical Equal-Area Projection Oblique Case Map of the World.png|400px|thumb|Cylindrical equal-area projection with oblique orientation]]
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| In [[cartography]], the '''cylindrical equal-area projection''' is a family of [[Map projections#Cylindrical|cylindrical]], [[Map projection#Equal-area|equal area]] [[map projection]]s.
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| ==Cylindrical projections==
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| {{Main|Map_projection#Cylindrical|l1=Cylindrical map projection}}
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| The term "normal cylindrical projection" is used to refer to any projection in which [[Meridian (geography)|meridians]] are mapped to equally spaced vertical lines and [[circles of latitude]] (parallels) are mapped to horizontal lines (or, [[mutatis mutandis]], more generally, radial lines from a fixed point are mapped to equally spaced parallel lines and concentric circles around it are mapped to perpendicular lines).
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| The mapping of meridians to vertical lines can be visualized by imagining a cylinder (of which the axis coincides with the Earth's axis of rotation) wrapped around the Earth and then projecting onto the cylinder, and subsequently unfolding the cylinder. | |
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| By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the [[Trigonometric function|secant]] of the [[latitude]] as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ):
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| The only cylindrical projections that preserve area have a
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| * North-south compression precisely the reciprocal of east-west stretching (cosine φ): equal-area cylindrical (with many named specializations such as [[Gall–Peters projection|Gall–Peters]] or Gall orthographic, [[Behrmann projection|Behrmann]], and [[Lambert cylindrical equal-area projection|Lambert cylindrical equal-area]]). This divides north-south distances by a factor equal to the secant of the latitude, preserving area but heavily distorting shapes.
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| Any particular cylindrical equal-area map has a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale.
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| ==Description==
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| ===Formulae===
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| All cylindrical equal-area projections use the formula:
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| :<math>x = ( \lambda - \lambda_0 ) \cos \phi_0\,</math>
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| :<math>y = \sin \phi / \cos \phi_0\,</math>
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| where <math>\lambda\,</math> is the longitude, <math>\lambda_0\,</math> is the central meridian, <math>\phi\,</math> is the latitude, and <math>\phi_0\,</math> is the standard latitude,<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.76–85</ref> all expressed in radians.
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| Some cartographers prefer to work in degrees, rather than radians, and use the equivalent formula:
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| :<math>x = ( \lambda - \lambda_0 ) (\cos \phi_0) \pi / 180^\circ</math>
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| :<math>y = \sin \phi / \cos \phi_0\,</math>
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| ===Simplified formula===
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| Stripping out unit conversion and uniform scaling, the formulae may be written:
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| :<math>x = ( \lambda - \lambda_0 ) S\,</math>
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| :<math>y = \sin\phi\,</math>
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| Hence the sphere is mapped onto a stretched vertical cylinder. The stretch factor S is what distinguishes the variations of cylindric equal-area projection.
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| ===Discussion===
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| The various specializations of the cylindric equal-area projection differ only in the ratio of the vertical to horizontal axis. This ratio determines the ''standard parallel'' of the projection, which is the parallel at which there is no distortion and along which distances match the stated scale. There are always two standard parallels on the cylindric equal-area projection, each at the same distance north and south of the equator. The standard parallels of the Gall–Peters are 45° N and 45° S. Several other specializations of the equal-area cylindric have been described, promoted, or otherwise named.<ref name="Snyder2">Snyder, John P. (1989). ''An Album of Map Projections'' p. 19. Washington, D.C.: U.S. Geological Survey Professional Paper 1453. (Mathematical properties of the Gall–Peters and related projections.)</ref><ref name="Monmonier">Monmonier, Mark (2004). ''Rhumb Lines and Map Wars: A Social History of the Mercator Projection'' p. 152. Chicago: The University of Chicago Press. (Thorough treatment of the social history of the Mercator projection and Gall–Peters projections.)</ref><ref name="Smyth">Smyth, C. Piazzi. (1870). ''On an Equal-Surface Projection and its Anthropological Applications''. Edinburgh: Edmonton & Douglas. (Monograph describing an equal-area cylindric projection and its virtues, specifically disparaging Mercator's projection.)</ref><ref>
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| Weisstein, Eric W. "Cylindrical Equal-Area Projection." From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/CylindricalEqual-AreaProjection.html
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| </ref>
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| {| class="wikitable"
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| |+Named specializations of the cylindrical equal-area projection
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| |-
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| ! Projection
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| ! Image
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| ! Creator<br>(year)
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| ! Standard parallels N/S
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| ! Width/height aspect ratio
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| ! Notes
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| |-
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| | cylindrical equal-area || || || <math>\phi_0\,</math>
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| | <math>\pi(\cos \phi_0)^2\,</math>
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| | Base projection for all the others.
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| |-
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| | [[Lambert cylindrical equal-area projection|Lambert]]
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| | [[File:Tissot indicatrix world map Lambert cyl equal-area proj.svg|150px]]
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| | [[Johann Heinrich Lambert]]<br>(1772)
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| | Equator (0°)
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| | <math>\pi \approx 3.14</math>
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| | [[Behrmann projection|Behrmann]]
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| | [[File:Tissot indicatrix world map Behrmann equal-area proj.svg|150px]]
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| | Walter Behrmann<br>(1910) || 30°
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| | <math>3\pi/4 \approx 2.36 \approx</math> [[silver ratio|<math>\delta_S</math>]] ||
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| | [[Smyth equal-surface]]<br>= Craster rectangular || || [[Charles Piazzi Smyth|Charles Piazzi Smyth]]<br>(1870) || 37°04'
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| | <math>2.0</math> ||
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| |-
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| | Trystan Edwards || || Trystan Edwards (1953) || 37°24'
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| | <math>\approx 2.0</math> ||
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| |-
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| | [[Hobo–Dyer projection|Hobo–Dyer]]
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| | [[File:Tissot indicatrix world map Hobo-Dyer equal-area proj.svg|150px]]
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| | Mick Dyer<br>(2002) || 37°30'
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| | <math>\approx 2.0</math> ||
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| |-
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| | [[Gall–Peters projection|Gall–Peters]]<br>= Gall orthographic<br>= Peters
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| | [[File:Tissot indicatrix world map Gall-Peters equal-area proj.svg|150px]]
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| | [[James Gall]]<br>(1855)
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| | 45°
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| | <math>\pi/2 \approx 1.57 </math>
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| | Promoted by Arno Peters as a new invention in 1967.
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| | Balthasart || || M. Balthasart<br>(1935) || 50°
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| | <math>\approx 1.3</math>
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| | Tobler's world in a square || || [[Waldo Tobler]] (1993) || 55.65°
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| | <math>1.0</math>
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| |}
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| ==History==
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| The invention of the Lambert cylindrical equal-area projection is attributed to the [[Alsace|Alsatian]] mathematician [[Johann Heinrich Lambert]] in 1772.<ref name="mulcahy_lambert">{{cite web
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| | last =Mulcahy
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| | first =Karen
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| | authorlink =
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| | coauthors =
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| | title =Cylindrical Projections
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| | work =
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| | publisher = [[City University of New York]]
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| | date =
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| | url =http://www.geo.hunter.cuny.edu/mp/cylind.html
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| | doi =
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| | accessdate = 2007-03-30 }}</ref> Variations of it appeared over the years by inventors who stretched the height of the Lambert and compressed the width commensurately in various ratios. See [[#Discussion|Named specializations]] table.
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| The [[Tobler hyperelliptical projection]], first described by Tobler in 1973, is a further generalization of the cylindrical equal-area family.
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| The [[HEALPix]] projection is an equal-area hybrid combination of: the Lambert cylindrical equal-area projection, for the equatorial regions of the sphere; and an interrupted Collignon projection, for the polar regions.
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| ==See also==
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| *[[Lambert azimuthal equal-area projection]]
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| *[[Lambert conformal conic projection]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections], from radicalcartography.net
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| * [http://www.uff.br/mapprojections/LambertCylindricalEqualArea_en.html An interactive Java Applet to study the metric deformations of the Lambert Cylindrical Equal-Area Projection].
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| {{Map Projections}}
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| [[Category:Cartographic projections]]
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| [[ca:Projecció cilíndrica equivalent]]
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| [[nl:Orthografische cilinderprojectie]]
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| [[ja:ランベルト正積円筒図法]]
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| [[sv:Lamberts cylindriska ytriktiga projektion]]
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This should be followed by a thorough check over for damage. Make a conscious effort to check out tire tread performance under various conditions. The trail then follows the side of the glacial Lake Pukaki through to Twizel, the town build in the 60s only to house workers from the Waitaki Hydroelectricity Scheme. If the skin diameter is smaller than a quarter do not be surprised if you must change them a couple of instances per season to keep the bike working reliably. If you have any queries with regards to where and how to use Biking for modern life mountain bike sizing., you can get hold of us at the internet site. Two hunters may choose to use trailers if their distance from the truck is over four or five miles.
There are also single speed mountain bikes that only have one set gear ratio. After their devastating loss to the Dallas Mavericks, there has been a lot of question as to whether they are really capable of winning a title or not. David Moffat founded Winter Park as a workers camp during construction of the Moffat Tunnel while building the transcontinental railroad from Denver to the Pacific. Cost shouldn't be a factor as a good helmet can be acquired for around $25-$45. Full suspensions are of course the most comfortable.
Technological know-how is advancing very rapidly and manufactures have observed ways to make batteries much more efficient and Eco-pleasant at the very same time along with photo voltaic PV cells getting additional and a lot more effortless and economical to make. Here are some of the more popular mountain bike wheels now available [*CO]. The tape (or string against the ruler) will indicate what your helmet size is. Follow these simple tips and maximize your riding time while you wait for the snow to fall again. The suitable quill stems are sized down to the internal diameter of your fork's steer tube.
When discount sales are on, you need to be sure you understand the terms and conditions of your purchase, including warranty information. You can surpass your rivals if you participate in a match. In the purest sense of the word, a mountain bikes sole mission is to travel "off-road" only. Now do your comparison-shopping based on five or six available bikes. To help you choose which one you to buy, here are the list of bikes and their use.
I ran with Hale and we also tried this method, it was effective. They get used on the street which is not what it's built for. Are you going to be going up and down hills, across flat terrain, on cement, or through rough and rocky areas. Hence, XC suspension forks tend to have a short travel and are light weight. They will provide you with a honest price, yet be ready to pay in between $650 and $4,000 on dual suspensions and in between $470 and $670 for hardtails.