Eckert IV projection
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![{\displaystyle {\begin{aligned}x&={\frac {2}{\sqrt {4\pi +\pi ^{2}}}}R\,(\lambda -\lambda _{0})(1+\cos \theta )\approx 0.422\,2382\,R\,(\lambda -\lambda _{0})(1+\cos \theta ),\\[8pt]y&=2{\sqrt {\frac {\pi }{4+\pi }}}R\sin \theta \approx 1.326\,5004\,R\sin \theta ,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f23e7d33107851d02f860589a7fb5a4eee05f749)
![{\displaystyle {\begin{aligned}\theta &=\arcsin \left[y{\frac {\sqrt {4+\pi }}{2{\sqrt {\pi }}R}}\right]\approx \arcsin \left[{\frac {y}{1.326\,5004\,R}}\right]\\[8pt]\varphi &=\arcsin \left[{\frac {\theta +\sin \theta \cos \theta +2\sin \theta }{2+{\frac {\pi }{2}}}}\right]\\[8pt]\lambda &=\lambda _{0}+x{\frac {\sqrt {4\pi +\pi ^{2}}}{2R(1+\cos \theta )}}\approx \lambda _{0}+{\frac {x}{0.422\,2382\,R\,(1+\cos \theta )}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4dc58f1e467ea9369202d3b0a67c7e3f2e8a9842)
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