A 1-D sphere is 2 points equidistant (by a radius) from a third point (the centre), not a line. Which is exactly what you get when you cut a circle with a plane passing through the centre of the circle, but not coplanar with the circumference. It is still the locus of all points equidistant from the centre.
A 1-D sphere is 2 points equidistant (by a radius) from a third point (the centre), not a line. Which is exactly what you get when you cut a circle with a plane passing through the centre of the circle, but not coplanar with the circumference. It is still the locus of all points equidistant from the centre.