Draw a plane and a line through the center of a sphere. What if the plane or the line do not pass through the center of the sphere?
See solution.
Practice makes perfect
First, we will describe the number of types of planes that produce reflection symmetry in a sphere. Then, we will describe the angles of rotation that produce rotation symmetry in the sphere.
Reflection Symmetry
First, let's analyze a sphere and a plane that do not pass through the center of the sphere.
Note that in this case no such plane will produce reflection symmetry in the sphere. However, the situation changes radically if we consider any plane passing through the center of the sphere.
We can see that there are infinitely many planes that produce reflection symmetry in a sphere. Each such plane passes through the center of the sphere.
Rotation Symmetry
Just like before, let's first analyze a sphere and a line that does not pass through the center of the sphere.
Note that in this case no such line will produce rotation symmetry in the sphere by any angle. Now, let's analyze a line passing through the center of the sphere.
This tells us that there are infinitely many lines that produce rotation symmetry in a sphere. Each such line passes through the center of the sphere and a sphere can be mapped onto itself by a rotation of any angle about the line.
