Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Circular chess advance only opens one square for the bishop. Some players advance the central pawns first anyway, while others prefer to advance the rooks' pawns in order to open lines of attack for the more powerful pieces; it is not known which move, if any, is objectively best. The different geometry of the square and circular boards creates considerable differences in endgame theory: three of the four "basic checkmates" on a square board (those with king and rook, king and two bishops, or king and bishop and knight against a lone king) rely on forcing the defending king into the corner