- #1

bers

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can I say that a sphere is a plane, because in spherical coordinates, I can simply express it as [itex]<(r, \theta, \varphi)^T, (1, 0, 0)^T> = R[/itex]? It does sound too easy to me. I'm asking because I'm thinking about whether it is valid to generalize results from the John-Radon transform (over k-planes in an n-dimensional space) to curvilinear coordinates. In the book I'm reading (Analytic tomography), a k-plane is the set of points x in ℝ

^{n}with [itex]<x, u> = c[/itex], with c real and u any unit vector in ℝ

^{n}. Clearly, R is real and [itex](r, \theta, \varphi) = (1, 0, 0)^T[/itex] is a unit vector in ℝ

^{n}.

Thanks

bers