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June 29

A curving funnel going into itself...?

Hello ever-helpful reference desk people; I've had this image in my mind lately, and I'm not sure if I imagined it or saw it somewhere--and I'm not even sure how to envision it, really, but I feel like it's envision-able and perhaps easily representable in some mathematical way (I am mathematically illiterate, unfortunately): Picture a funnel, descending and curving around to go back into itself. Would this create an "endless" sort of flattened nautilus? Can anyone help me towards seeing this thing, or otherwise straighten my head out here? Much obliged, as always! — Preceding unsigned comment added by 99.32.190.71 (talk) 00:15, 29 June 2012 (UTC)[reply]

Something Klien bottle-ish? --Tagishsimon (talk) 00:22, 29 June 2012 (UTC)[reply]

Or he might be thinking of a pseudosphere, or more precisely an immersion of (part of a) pseudosphere into 3-space. --Trovatore (talk) 00:27, 29 June 2012 (UTC)[reply]

The description looks more to me like a spiral toroid. http://ladygogogoch.blogspot.com/2010/06/einstein-ring.html is a page that shows an M. C. Escher etching of one, and http://soukoreff.com/gnuplot/ is a page that shows a plotted one, calling it a "conic spiral". Looie496 (talk) 01:35, 29 June 2012 (UTC)[reply]

The spiral toroid was just what I was picturing--thanks a lot! --OP