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.

CAPTCHA
This question is for testing whether you are a human visitor and to prevent automated spam submissions.