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Gabriel's Horn - Sankarshan Bhattacharyya

Gabriel’s horn (also known as Torricelli’s trumpet) is a hypothetical solid of revolution that ostensibly has infinite surface area but finite volume.

It is modelled by the function y=1x (1≤x<∞), which is rotated 360° or 2π radians around the x-axis. The special mathematical properties of Gabriel’s horn are the key inspiration for the legendary painter’s paradox.

Figure I: Gabriel’s Horn

I should caution readers that the following content consists of mathematics that is typically suitable for Year 12 and Year 13 students with a suitable degree of mathematical dexterity.