- #1
Illuminatum
- 8
- 0
Hi all,
Perhaps I'm asking the wrong question but I am wondering about the relationship between different definitions of, for the sake of argument, the torus.
We can define it parametrically (or as a single constraint) and from there work out the induced metric as with any surface.
But we can also define it by considering the plane and identifying opposite sides. Is it possible to use this definition, equip the plane with Cartesian coordinates and then deduce the metric on the torus caused by the identification?
I hope I've explained myself and apologise if it's an ill-thought-out question.
Thanks,
I
Perhaps I'm asking the wrong question but I am wondering about the relationship between different definitions of, for the sake of argument, the torus.
We can define it parametrically (or as a single constraint) and from there work out the induced metric as with any surface.
But we can also define it by considering the plane and identifying opposite sides. Is it possible to use this definition, equip the plane with Cartesian coordinates and then deduce the metric on the torus caused by the identification?
I hope I've explained myself and apologise if it's an ill-thought-out question.
Thanks,
I