It is known that we need at least 3 points to fix a circle. i.e. In coordinate geometry, it require three pairs of coordinates to find out the equation of the circle; and in geometry it requires three points to fix the radius and center of a circle.
Now consider what happened in 3 dimensions space. In coordinate geometry, it require three equations of circle to find out the equation of the sphere; and in geometry it requires four points to fix the radius and center of a sphere.
Could we therefore extend this analogy: In 4 dimensions space, it require 4C3=4 equations of sphere in 3 dimensions to find out the equation of the sphere in 4D; and in geometry it requires four sphere in 3D to fix the radius and center of a sphere in 4D?
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