  Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian
spacetime, such as the Schwarzschild radial line element, I find another
metric, but with Euclidean signature, which produces the same geodesics x(t).
This geodesically equivalent, or dual, metric can be embedded in ordinary
Euclidean space. On the embedded surface freely falling particles move on the
shortest path. Thus one can visualize how acceleration in a gravitational field
is explained by particles moving freely in a curved spacetime. Freedom in the
dual metric allows us to display, with substantial curvature, even the weak
gravity of our Earth. This may provide a nice pedagogical tool for elementary
lectures on general relativity. I also study extensions of the dual metric
scheme to higher dimensions. In an addendum I extend the analysis concerning
the shape of an embedding of the dual spacetime of a line through a planet of
constant proper density.
