Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?

[ijabbott]

(02-06-2019 08:31 AM)Thomas Klemm Wrote:  

(02-05-2019 11:04 PM)Vtile Wrote:  PS. Give me Gabriel's horn and I will show how to paint it with finite amount of paint. Easy just fill it with exactly the volume amount of paint and all the surface area is painted. Prove that I'm wrong.

Quote:This leads to the paradoxical consequence that while Gabriel's horn can be filled up with \(\pi\) cubic units of paint, an infinite number of square units of paint are needed to cover its surface!

You're not wrong. Still the area is infinite. Which makes it paradox as it contradicts our everyday experience of how paint works.

You just need an infinitesimal layer of paint.