Plucker Sentence Examples
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.Advertisement
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).Advertisement
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.Advertisement
According to Plucker, the coefficient of cubical dilatation at moderately low temperatures is 0.0001585.
The title of his "habilitationsschrift," Generalem analyseos applicationem ad ea quae geometriae altioris et mechanicae basis et fundaments sunt e serie Tayloria deducit Julius Plucker (Bonn, 1824), indicated the course of his future researches.
In the first volume of this treatise Plucker introduced for the first time the method of abridged notation which has become one of the characteristic features of modern analytical geometry (see Geometry, Analytical).
Allied to the matter just mentioned was Plucker's discovery of the six equations connecting the numbers of singularities in algebraical curves (see Curve).
Plucker communicated his formulae in the first place to Crelle's Journal (1834), vol.Advertisement
Certain ancient stringed instruments were played with a plectrum or plucker made of the quill of a bird's feather, and the word has thus been used of a plectrum made of other material and differing in shape, and also of an analogous object for striking the strings in the harpsichord, spinet or virginal.
For the investigation of the spectra of gases at reduced pressures the so-called Plucker tubes (more generally but incorrectly called Geissler tubes) are in common use.
When, for instance, we observe the relation of the gas contained in a Plucker tube through which an electric discharge is passing, there can be little doubt that the partition of energy is very different from what it would be in thermal equilibrium.
According to circumstances, the colour of the light obtained from a Plucker vacuum tube changes "from red to a rich steel blue," to use the words of Crookes, who first described the phenomenon.