Hopefully I can justify the reasoning behind this with the following: A circle is defined as the set of all points in a 2-dimensional space equidistant to a gi

Hopefully I can justify the reasoning behind this with the following: A circle is defined as the set of all points in a 2-dimensional space equidistant to a given center point (the distance being the circle's radius). A sphere is defined as the set of all points in a 3-dimensional space equidistant to a given center point. A line in 1-d does not analogize to this definition but a point does.