Given an open spherical polygon of geodesic edge length $L_i$ ($i=0,..,n$) and anterior spherical angles $A_i$ ($i=0,..,n-1$). My question is what are sufficient and nessecary conditions on the lengths of arcs $L_i$ and on $A_i$ for the closure of that polygon?
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What have you tried? What's an "open spherical polygon"? – David G. Stork Aug 05 '20 at 17:53
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I mean by open spherical polygon a sequence of points P_i (i=0,..,n) on S^2 with P_0 is different to P_n. What i m looking for is conditions on Lengths and angles (spherical) that guanties P_0=P_n . – Mohamed Bellaihou Aug 05 '20 at 18:18
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Anterior is supplement to interior angle? – Narasimham Aug 05 '20 at 19:46
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Are points P_i in a plane? Anterior is supplement to interior angle? – Narasimham Aug 05 '20 at 19:49
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So what is the difference between and "open" and a "closed" spherical polygon? – David G. Stork Aug 05 '20 at 20:01