Re: Sphere

mr why wrote:
Yes you are right 14 vs 15 after 4 cuts
The extra one is the internal tetrahedron. The other 14 show on the spherical surface.
It is very interesting that after 4 cuts we begin to populate TWO classes of pieces. "Internal" and "surface" pieces.

A spherical shell is your surface!
Of course when I said a sphere I meant a solid! How else can the area of a triangle be half base times height!!! To say that area is merely that enclosed by the periphery of the triangle is very clumsy.

The number of pieces after n cuts of a spherical shell thickness t is an even more interesting question.

The problem with "ball" is few are round - especially in the US! And a ball of twine is not even filled.

It depends whether you want maths to have its own jargon, or to use the words used by other people in normal language.

It isn't a matter of jargon, it's a matter of precision. This is a maths group, after all.
.