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

[Massimo Gnerucci]

(01-31-2019 09:29 PM)rprosperi Wrote:  

(01-31-2019 06:47 PM)Valentin Albillo Wrote:  Well, the mathematical 3D object called Gabriel's Horn has finite volume but infinite area.

That would surely maximize area/volume.

(01-31-2019 06:56 PM)Thomas Klemm Wrote:  Gabriel's Horn has finite volume but infinite surface area:

Whoa, that's the coolest thing, that I can't fully process, that I've heard all week.

From the linked article:

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!

Thanks for the thought provoking question and these answers.

And now... how the heck do ya hold this thing up to paint it....

Well, the inner surface should be already painted up once you fill it, no?