Do determine a circle, you would need at least three coordinates. How many are necessary to determine a sphere?
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I believe the answer is 4 (and hopefully someone will correct me if I'm wrong...). Here's why. Any 3 points are coplanar. Consider 3 points on the plane A, B, and C. One can connect each pair of points with a line segment to create a triangle, then circumscribe a circle. The center of said circle is equidistant to all 3 points. Consider a line passing through the center perpendicular to this plane. It is easy to prove that any point on this line is also equidistant from A, B, and C. Therefore, it must take more than 3 points to determine a sphere.
A nice explanation for 4. 3 gives you a circle. But you need one more to determine the size of the circle compared to the sphere.