I would like to show someone the domain of the complex square root function (the 2-sheeted riemann surface). Is there a good interactive visualization software for this?
I would like some sort of GeoGebra style app where there is a forbidden point or disk, but outside of that you can drag a point around. As you drag around the pole, it changes from red to blue smoothly, so that on the bottom sheet it is red, and on the top sheet it is blue (or some reasonable periodic color scheme where 50% apart is always very distinct).
It would be doubly nice if one could have simple geometric shapes do the same. Basically I want a nice double covering of a plane symmetry group that is still very geometric.
It would be n-tuply nice if one could handle nth roots and the n-sheeted Riemann surface, but n=2 suffices for me, I think.
I've used other people's geogebra apps, but never made my own, and have no idea how to keep track of what sheet the point is on (or honestly how to animate the color, though I assume once I have a 0…4π valued argument function, I should be fine).
Some pretty images from wikipedia: