English: In the spacetime diagram on the left, the magenta hyperbolae connect events of equal spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation from the origin. When viewed with an extra dimension of space, these respectively generate hyperboloids of one sheet and two sheets.
Note a confusing point of nomenclature: The magenta hyperbolae, which cross the x axis and represent loci of points separated by constant spacelike distances from the origin, are termed "timelike" (not spacelike) hyperbolae because all intervals along the hyperbola are timelike intervals. Likewise the green hyperbolae, which cross the ct axis, are termed "spacelike" hyperbolae because all intervals along the hyperbolae are spacelike intervals.