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.