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Canonical coordinates

Hi, the sentence below is a sentence from a book on canonical coordinates:

'If a curve of constant s and a curve of constant r meet at a point, they cross one another transversely'

I don't really understand what this means, if someone could explain this more clearly that would be great. First of all what is a curve of constant r and a curve of constant s? Are these curves that have the form r(x,y) = a and s(x,y) = b, where a and b are constants? Also what does it mean by transversely?

Thanks for your help.
For any coordinate system, the 'grid' from it's lines, while possibly weird and curvy, is made from lines where one coordinate is fixed. In cartesian, we could see the y axis as the curve (x(t)=0, y(t)=t), a curve of constant x, and vice versa for the x axis. In polars, you can have curves of fixed theta (fix theta, choose any r), or a ring of fixed r (fix r, choose any theta).

I'm not sure what transversely means.
Original post by FireGarden
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OP really needs to reference the book he's using - there is a diagram!

See here

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