Paradox of Gabriels horn or the infinite paint can. Though we cannot prove it here, the

Chapter 5, Problem 26

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Paradox of Gabriels horn or the infinite paint can. Though we cannot prove it here, the surface area of Gabriels horn (see Exercise 25) is given by Show that the surface area of Gabriels horn does not exist. The paradox is that the volume of the horn exists, but the surface area does not. This is like a can of paint that has a finite volume but, when full, does not hold enough paint to paint the outside of the can.

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