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Do you need the implicit function theorem? Can you give an explicit charts?

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closed as too localized by Qiaochu Yuan, Deane Yang, Mariano Suárez-Alvarez, Angelo, Willie Wong Jan 22 '11 at 16:33

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Please post on It's a good question (because there are lots of different good answers) but not for here. – Deane Yang Jan 22 '11 at 15:36
This is somewhat off-topic for MO. You should ask somewhere like – Qiaochu Yuan Jan 22 '11 at 15:37

Euler angles give the parametrization and the charts.

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