Question

How many great circles can a sphere have

Answer 1

Answer:

infinitely many

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Answer 2

Answer:

Infinite

To find:

Show that set of all rational numbers is not a closed set and also it is not an open set.

Solution:

A great circle in a sphere is the largest circle you can draw on it. The center of a great circle is also the center of the sphere.

You need only one great circle to define a sphere in 3 dimensions. Simply draw an axis through the center and circumference of the circle and rotate it about this axis to generate the whole sphere.

Since each different rotation of the circle is still a great circle on the sphere, we see that there are infinitely (and uncountably) many great circles on a given sphere.

Conclusion:

Hence, there can be infinite number of great circles on a sphere.

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