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Changing Sqrt{(z-1)(z-2)(z-3)} to coffee mug
*To*: mathgroup at smc.vnet.net
*Subject*: [mg82698] Changing Sqrt{(z-1)(z-2)(z-3)} to coffee mug
*From*: chuck009 <dmilioto at comcast.com>
*Date*: Mon, 29 Oct 2007 05:30:48 -0500 (EST)
I sure would like to see animation of this over the Riemann sphere: Take two Riemann spheres corresponing to the two branches of sqrt showing the two branch cuts on each. Now: open up the branch cuts, stretch them into necks, join the necks, form the double flask, double neck, transform this into a donut, indent the donut into a coffee mug. Would make a nice addition to the Wolfram demonstration project.
I can only get as far as using ContourPlot3D with the two holes in the sphere:
r2 = ContourPlot3D[x^2 + y^2 + z^2 == 2, {x, -2, 2},
{y, -2, 2}, {z, -2, 2}, RegionFunction ->
Function[{x, y, z}, (x - 0.2)^2 + (y - 0.2)^2 > 0.05 &&
(x - 0.7)^2 + (y - 0.7)^2 > 0.05],
BoundaryStyle -> Directive[Red, Thick], Boxed -> False,
Axes -> None]
Anyone know of this being done or how one might do this?
Thanks,
Chuck
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