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Thought Experiment in Mathematics: Gabriel's Horn
- kafkaesq 10y agoOne 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.