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Doughnuts appear in a number of mathematically classifiable forms,
predominantly oblate spheroids and ellipsoids, cylinders with domed
ends, and toroids.
The logical progression is to label them not as "ring" or "filled" but by
the set of equations that describes their form.
This would be
immensely satisfying to mathematicians, physicists,
engineers and geeks of all sorts, as questions such as "Do I
sugar dusting on a small torus or a larger spheroid ?" can be
unambiguously resolved before approaching the counter.
Not really relevant
Spotted in a local bakery window, I think I posted this image before [pocmloc, Apr 02 2014]
||The sugar-dusting answer is obvious. You need a
Sierpinski donut fractal with infinite surface area but
volume. Infinite amount of sugar dusting but zero
||I think that donut should be alternately spelled "doughnut", but this idea renders that spelling reform redundant.
||Phew! Just think how many arguments your idea has prevented. Almost enough to warrant a Nobel Peace Prize.
||[+] for helping to force those whose maths (which one should quite often call "math") fell somewhere short of topology to resume their quest.