- #1
Spinnor
Gold Member
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Surface like helicoid in S^3?
Consider the surface of a helicoid in cylindrical coordinates:
z = phi , see for example:
http://images.google.com/images?hl=en&q=helicoid&btnG=Search+Images&gbv=2
Now say I'm sitting in the space S^3 whose radius is much larger then my height. I hold the truncated surface of a helicoid in my hand.
Does this surface "extend" to all of S^3 in some natural way? Is there a simple function for this helicoid like z = phi?
Thanks for any help.
Consider the surface of a helicoid in cylindrical coordinates:
z = phi , see for example:
http://images.google.com/images?hl=en&q=helicoid&btnG=Search+Images&gbv=2
Now say I'm sitting in the space S^3 whose radius is much larger then my height. I hold the truncated surface of a helicoid in my hand.
Does this surface "extend" to all of S^3 in some natural way? Is there a simple function for this helicoid like z = phi?
Thanks for any help.