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The surface of a sphere is defined in that manner.

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Q: What is a three-dimensional figure with all points equidistant from a single point?
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All the points on a plane that are equidistant from a single point?

All points on the circumference of a circle drawn on a plane are equidistant from the single point on the plane which is the center of the circle.


How do you best describe a parabola?

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A circle is a set of points equidistant ( the same distance ) away from a single point, the center of the circle.


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How many surface does a sphere have?

A sphere has a single curved surface. It is said to have one surface. Further, the sphere has no "flat spots" or "angles" or "discontinuities" of any kind. It is a planar figure that is the set of all points equidistant from a single point, which is its center.A sphere has only one surface.


What is a figure where all the points are the same distance from a single point?

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Group theory is of particular significance to the study of objects having plenty of symmetry. The sphere is a good example; its self-equivalences include arbitrary rotations in three dimensions about the centre.Notice that for any two points on the sphere, there is a self-equivalence (i.e., rotation) taking one of the points to the other.The sphere is homogeneous, a technical word meaning "having lots of symmetry"! A special role is played by the set of self-equivalences fixing a single point (in this case, the rotations about a fixed axis); it is called the isotropy subgroup of the symmetry.


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