What is pi times pi?
Answered by Alexander Farrugia, Quora contributor.
The persons who define π as the area of a circle of unit radius may like the following definition of π squared:
It is the surface area of the horn torus whose tubing is of unit diameter — in other words, the surface area of the following shape, assuming the two circles of its vertical cross section have unit diameter:
I thought you might like to see this pretty gif.
Image captured from Wolfgang W. Daeumler @