
Thought Experiment in Mathematics: Gabriel's Horn - micaeloliveira
http://fermatslibrary.com/s/gabriels-horn
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kafkaesq
One of the interesting aspects of Gabriel's Horn is that the volume of the
rotation of the curve _x → 1 /x_ is finite, even though the area under the
curve itself (restricted to single plane) is infinite. Which isn't deeply
surprising, but can seem a bit strange if you're new to 3D geometry and
calculus.

So being able to quickly navigate relations (and apparent contradictions) like
these without pausing to turn the crank and do the integral calculus -- "yeah,
the volume is basically the integral of the square of _1 /x_, therefore it's
bounded" \-- is really quite crucial.

