Is a Sphere 2-D or 3-D? Date: 8/8/96 at 10:38:39 From: Janice
Behrens Subject: Is a Sphere 2-D or 3-D? Dear Dr. Math: Is a
sphere a two- or a three-dimensional object? Date: 9/1/96 at
17:26:49 From: Doctor Jerry Subject: Re: Is a Sphere 2-D or 3-D?
Just to be certain we mean the same thing by sphere, a sphere is
the set of all points in space (or R^3, which is Euclidean three
space) at an equal distance from a fixed point. Not a solid
ball. Although the sphere is a subset of three-dimensional
space, it is a two-dimensional object. A circle can exist in
either two-dimensional or three-dimensional space (or even
higher-dimensional spaces), but it is a one-dimensional object.
A line segment, which is one-dimensional, can be deformed into a
circle. We can think of the line as elastic. A circular disk,
which is two-dimensional, can be deformed elastically into a
sphere. If you know about describing curves and surfaces
parametrically, then, with certain restrictions, the dimension
of the object is equal to the numb