View source for Kavrayskiy VII projection

[[File:Kavraiskiy VII projection SW.jpg|350px|thumb|Kavrayskiy VII projection of the [[Earth]]]]
[[File:Kavrayskiy VII with Tissot's Indicatrices of Distortion.svg|350px|thumb|The Kavrayskiy VII projection with [[Tissot's indicatrix]] of deformation]]

The '''Kavrayskiy VII projection''' is a [[map projection]] invented by Soviet cartographer [[Vladimir V. Kavrayskiy]] in 1939<ref name="Snyder"/> for use as a general-purpose pseudocylindrical projection. Like the [[Robinson projection]], it is a compromise intended to produce good-quality maps with low distortion overall. It scores well in that respect compared to other popular projections, such as the [[Winkel tripel projection|Winkel tripel]],<ref name="Goldberg-Gott"/><ref name="Capek"/> despite straight, evenly spaced [[Parallel (latitude)|parallels]] and a simple formulation. Regardless, it has not been widely used outside the former [[Soviet Union]].{{citation needed|date=April 2016}}

The projection is defined as

: <math>\begin{align}
 x &= \frac{3 \lambda}{2} \sqrt{\frac{1}{3} - \left(\frac{\varphi}{\pi}\right)^2}, \\
 y &= \varphi,
\end{align}</math>

where ''λ'' is the [[longitude]], and ''φ'' is the [[latitude]] in radians.

==See also==

* [[List of map projections]]
* [[Cartography]]
* [[Wagner VI projection]]
* [[Robinson projection]]

==References==
{{Reflist|refs=
<ref name="Snyder">{{cite book
  | title      = Flattening the Earth: Two Thousand Years of Map Projections
  | last       = Snyder
  | first      = John P.
  | authorlink = John P. Snyder
  | year       = 1993
  | publisher  = University of Chicago Press
  | location   = Chicago
  | isbn       = 0-226-76747-7
  | pages      = 202
  | url        = https://books.google.com/books?id=0UzjTJ4w9yEC&lpg=PA282&pg=PA279
  | accessdate = 2014-11-05
  }}</ref>
<ref name="Goldberg-Gott">{{cite journal
  | url        = http://www.physics.drexel.edu/~goldberg/projections/goldberg_gott.pdf
  | title      = Flexion and Skewness in Map Projections of the Earth
  | year       = 2007
  | first1     = David M.
  | last1      = Goldberg
  | first2     = J. Richard
  | last2      = Gott III
  | journal    = Cartographica
  | volume     = 42
  | issue      = 4
  | pages      = 297–318
  | accessdate = 2014-11-05
  | doi=10.3138/carto.42.4.297
  | arxiv= astro-ph/0608501
  }}</ref>
<ref name="Capek">{{cite journal
  | last       = Capek
  | first      = Richard
  | year       = 2001
  | url        = http://icaci.org/documents/ICC_proceedings/ICC2001/icc2001/file/f24014.doc
  | title      = Which is the best projection for the world map?
  | journal    = Proceedings of the 20th International Cartographic Conference
  | location   = Beijing, China
  | volume     = 5
  | pages      = 3084–93
  | accessdate = 2014-11-05
  }}</ref>
}}

==External links==
{{Commons category|Maps with Kavrayskiy VII projection}}
* [http://www.physics.drexel.edu/~goldberg/projections/ Curvature in Map Projections], quantification of overall distortion in projections.
* [https://www.mapthematics.com/ProjectionsList.php?Projection=61#Kavraiskiy%20VII Mapthematics Kavrayskiy VII], bivariate distortion map.
* [http://www.progonos.com/furuti/MapProj/Normal/CartHow/HowKav7/howKav7.html Deducing the Kavrayskiy VII Projection], description of the properties of the Kavrayskiy VII projection.

{{Map Projections}}

[[Category:Map projections]]