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George Jones

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[tex]S^n \cong SO \left( n+1 \right)/SO \left( n \right)[/tex]

and

[tex]\mathbb{R}P^n \cong SO \left( n+1 \right)/O \left( n \right),[/tex]

so [itex]SO \left( 3 \right)/SO \left( 2 \right)[/itex] is isomorphic to the 2-sphere, and [itex]SO \left( 3 \right)/O \left( 2 \right)[/itex] is isomorphic to the projective plane.

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