Eckert IV Projection

Author

Eric W. Weisstein
April 19, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/MapProjections/EckertIVProjection.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EckertIVProjection.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Figure

V5

Show[Graphics[ProjectionPlot[Projection[EckertIV[]]]],AspectRatio->Automatic]//Timing

V6

Graphics[MapProjectionPlot[MapProjection[EckertIV[]]]]

Newton's Method

#/D[#,θ]&[θ+Sin[θ]Cos[θ]+2Sin[θ]-(2+(1/2)π)Sin[ϕ]]

Solve[θ+Sin[θ]Cos[θ]+2Sin[θ]==(2+(1/2)π)Sin[ϕ]&&0<θ<2π,θ]

Inverse

Solve[{x==(2/(Sqrt[π(4+π)]))(λ-λ0)(1+Cos[θ]),y==2(Sqrt[(π/(4+π))])Sin[θ]},{ϕ,λ}]

Solve[x==(2/(Sqrt[π(4+π)]))(λ-λ0)(1+Cos[θ]),λ]//FullSimplify