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does anyone know an explicit imbedding $h\colon T^2 \to \mathbb{R}^3$ of the torus $T^2=\mathbb{S}^1 \times \mathbb{S}^1$ into $\mathbb{R}^3$ ?

Thanks in advance !!!

Cheers...

2 Answers 2

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The standard parameterization is the one given on the top of the Wikipedia webpage for "torus".

http://en.wikipedia.org/wiki/Torus#Geometry

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    I see, you are right, i did not analyze the parameters $R,r$ to fully understand them and i thought that they should correspond to the radii of the two circles $\mathbb{S}^1×\mathbb{S}^1$ Thanks a lot again for your advice !!!!2012-03-08
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$(x,y)$ maps to $((3+\sin(y))\cos(x),(3+\sin(y))\sin(x),\cos(y))$