# Plucker sentence example

plucker
• Plucker aimed at furnishing modern geometry with suitable analytical methods so as to give it an independent analytical development.
• Plucker finally (Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice.
• In 1833 Plucker left Bonn for Berlin, where he occupied a post in the Friedrich Wilhelm's Gymnasium.
• In 1836 Plucker returned to Bonn as ordinary professor of mathematics.
• From this time Plucker's geometrical researches practically ceased, only to be resumed towards the end of his life.
• Hittorf tells us that Plucker never attained great manual dexterity as an experimenter.
• Induced by the encouragement of his mathematical friends in England, Plucker in 1865 returned to the field in which he first became famous, and adorned it by one more great achievement - the invention of what is now called "line geometry."
• Plucker himself worked out the theory of complexes of the first and second order, introducing in his investigation of the latter the famous complex surfaces of which he caused those models to be constructed which are now so well known to the student of the higher mathematics.
• Among the very numerous honours bestowed on Plucker by the various scientific societies of Europe was the Copley medal, awarded to him by the Royal Society two years before his death.
• We now come to Julius Plucker; his " six equations " were given in a short memoir in Crelle (1842) preceding his great work, the Theorie der algebraischen Curven (1844).
• Plucker first gave a scientific dual definition of a curve, viz.; " A curve is a locus generated by a point, and enveloped by a line - the point moving continuously along the line, while the line rotates continuously about the point "; the point is a point (ineunt.) of the curve, the line is a tangent of the curve.
• Plucker, moreover, imagined a system of line-co-ordinates (tangential co-ordinates).
• The whole theory of the inflections of a cubic curve is discussed in a very interesting manner by means of the canonical form of the equation x +y +z +6lxyz= o; and in particular a proof is given of Plucker's theorem that the nine points of inflection of a cubic curve lie by threes in twelve lines.
• The expression 2m(m - 2) (m - 9) for the number of double tangents of a curve of the order in was obtained by Plucker only as a consequence of his first, second, fourth and fifth equations.
• It was assumed by Plucker that the number of real double tangents might be 28, 16, 8, 4 or o, but Zeuthen has found that the last case does not exist.