# Can't get Element to work with Sphere

Mathematica returns

False

when I execute

Element[{0, 0, 0}, Sphere[{0, 0, 0}]]


whereas

 Element[{0, 0, 0}, Cuboid[]]


returns True as expected. Any clue why this could be happening?

Sphere is a two-dimensional object:

RegionDimension[Sphere[{0, 0, 0}]]
(* 2 *)


so its center is not included in the defined region. Only the shell is considered:

Element[Normalize@{1, 1, 1}, Sphere[{0, 0, 0}]]
(* True *)


You can use Ball instead:

RegionDimension[Ball[{0, 0, 0}]]
(* 3 *)

Element[{0, 0, 0}, Ball[{0, 0, 0}]]
(* True *)

• (+1) Another way to see sphere is not a solid is In[102]:= Refine[RegionMember[Sphere[], {x, y, z}], Element[{x,y,z}, Reals]] Out[102]= x^2 + y^2 + z^2 == 1 – Chip Hurst Sep 25 '16 at 1:55
• Ah, this clears it up, thanks. – Mike Sep 25 '16 at 2:07