In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in (n + 1)-dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. Thus, the n-sphere centred at the origin is defined by: It is an n-dimensional manifold in Euclidean (n + 1)-space. In particular: a 0-sphere is the pair of points at the ends of a (one-dimensional) line segment, a 1-sphere is the circle, which is the one-dimensional c...

Sarcasm is "a sharp, bitter, or cutting expression or remark; a bitter gibe or taunt." Sarcasm may employ ambivalence, although sarcasm is not necessarily ironic. "The distinctive quality of sarcasm is present in the spoken word and manifested chiefly by vocal inflections". The sarcastic content of a statement will be dependent upon the context in which it appears. == Origin of the term == The word comes from the Greek σαρκασμός (sarkasmos) which is taken from σαρκάζειν meaning "to tear flesh, bite the lip in rage, sneer". It is first recorded in English in 1579, in an annotation to The Shepheardes...