Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Scale (map)
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
====Lambert's equal area projection==== [[File:Tissot indicatrix world map Lambert cyl equal-area proj.svg|thumb|right|350px|Lambert's normal cylindrical equal-area projection with [[Tissot's indicatrix]] of deformation]] [[Lambert cylindrical equal-area projection|Lambert's equal area projection]] maps the sphere to a finite rectangle by the equations<ref name=snyder/><ref name=flattening/><ref name=merc/> :<math>x = a\lambda \qquad\qquad y = a\sin\varphi</math> where a, <math>\lambda</math> and <math>\varphi</math> are as in the previous example. Since <math>y'(\varphi)=\cos\varphi</math> the scale factors are : parallel scale <math>\quad k\;=\;\dfrac{\delta x}{a\cos\varphi\,\delta\lambda\,}=\,\sec\varphi\qquad\qquad{}</math> :meridian scale <math>\quad h\;=\;\dfrac{\delta y}{a\,\delta\varphi\,} = \,\cos\varphi</math> The calculation of the point scale in an arbitrary direction is given [[#Mathematical addendum|below]]. The vertical and horizontal scales now compensate each other (hk=1) and in the Tissot diagram each infinitesimal circular element is distorted into an ellipse of the ''same'' area as the undistorted circles on the equator.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)