Take the 2-minute tour ×  If there is no further specification
(such as solid or hollow), does a "sphere" refer to the
solid/filled form or the hollow shell?   share|improve this
question Since I use the definition "the set of all points in
space that are equidistant from a fixed point", then yes, the
shell. –  Ｊ. Ｍ. Sep 28 '11 at 16:16 add comment  2 Answers  up
vote 5 down vote accepted  In mathematics, the word "sphere"
refers to the hollow shell (see here). The word "ball" is
reserved for the solid version (see here).  So, for example, the
unit sphere in $\mathbb{R}^3$ is equal to the set
$$\{(x,y,z)\in\mathbb{R}^3\mid x^2+y^2+z^2=1\}$$ while the unit
ball in $\mathbb{R}^3$ is equal to the set
$$\{(x,y,z)\in\mathbb{R}^3\mid x^2+y^2+z^2\leq 1\}.$$  In common
usage of the word "sphere" in English, it could mean either.
share|improve this answer The solid is called a ball. –  lhf Sep
28 '11 at 15:57 @lhf: I'd just remembered to add that when you
posted your comment :) –  Zev Chonoles Sep 28 '11 at 16:00 Som