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- How is this expression of a torus?

In a differential geometry text, a torus is defined by the pair of equations:

I initially thought this was somehow a torus embedded in 4 dimensions, but I do not see how we can visualize two orthogonal 2-dimensional Euclidian spaces. How is this a representation of a 2 dimensional torus embedded in 3 dimensions, with 4 presumably orthogonal coordinates?

I initially thought this was somehow a torus embedded in 4 dimensions, but I do not see how we can visualize two orthogonal 2-dimensional Euclidian spaces. How is this a representation of a 2 dimensional torus embedded in 3 dimensions, with 4 presumably orthogonal coordinates?

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