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Sylvester–Gallai Theorem
The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the points or a line that passes through all of them. It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944. A line that contains exactly two of a set of points is known as an ''ordinary line''. Another way of stating the theorem is that every finite set of points that is not collinear has an ordinary line. According to a strengthening of the theorem, every finite point set (not all on one line) has at least a linear number of ordinary lines. An algorithm can find an ordinary line in a set of n points in time O(n\log n). History The Sylvester–Gallai theorem was posed as a problem by . suggests that Sylvester may have been motivated by a related phenomenon in algebraic geometry, in which the inflection points of a cubic curve i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Lines
Ordinary or The Ordinary often refer to: Music * ''Ordinary'' (EP) (2015), by South Korean group Beast * ''Ordinary'' (Every Little Thing album) (2011) * "Ordinary" (Two Door Cinema Club song) (2016) * "Ordinary" (Wayne Brady song) (2008) * "Ordinary", song by Train from ''Alive at Last'' (2004) Religion * Ordinary (Catholic Church), a supervisor, typically a bishop, in charge of a territory comparable to a diocese, or a major superior of a religious institute * Ordinary (church officer), an officer of a church or civic authority who by reason of office has ordinary power to execute laws * Ordinary (liturgy), a set of texts in Roman Catholic and other Western Christian liturgies that are generally invariable * Ordinary (lecture), a type of lecture given in universities of the Middle Ages Other * An archaic usage meaning tavern * ''Ordinary'' (film), a 2012 Malayalam-language film * Ordinary (heraldry), a simple geometrical figure displayed on a shield * Ordinary of arms, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
