Question regarding the Napkin Ring Problem
In mathematics, a napkin ring refers to the shape derived from subtracting a cylinder from a sphere. (the height of the cylinder is always large enough so there is only a ring-like shape left over)
While watching a Vsayce video on the napkin ring problem, (a problem which essentially proves that napkin rings with the same height always have the same volume regardless of the radius of the ciricle they were derived from, pretty elementary stuff) I came up with some questions regarding the shape and the problem.
Firstly, does the proof only apply to napkin rings that have perpendicular upper surfaces? Let's assume a wavy surface corresponding to a sin wave, would you be able to calculate relative periods?
Like, The heights vary along the rim of the napkin ring, yet it should be possible to calculate the sinosoidal of the any corresponding napkin ring of approximate average height, right?
Finally, And going off that, are draining vortex(es?) not just concentrically stacked variable height napkin rings that change according to increments?
I'd greatly appreciate an explanation.
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