Julius Plücker

Julius Plücker
Julius Plücker
Born	(1801-06-16)16 June 1801 Elberfeld,Duchy of Berg,Holy Roman Empire
Died	22 May 1868(1868-05-22)(aged 66) Bonn,Kingdom of Prussia
Nationality	German
Alma mater	University of Bonn University of Heidelberg University of Berlin University of Paris University of Marburg
Known for	Plücker's conoid Plücker coordinates Plücker embedding Plücker formula Plücker matrix Plücker relations Plücker surface Homogeneous coordinates
Awards	Copley Medal(1866)
Scientific career
Fields	Mathematics Physics
Institutions	University of Bonn University of Berlin University of Halle
Doctoral advisor	Christian Ludwig Gerling
Doctoral students	Felix Klein August Beer

Julius Plücker(16 June 1801 – 22 May 1868) was a Germanmathematicianandphysicist.He made fundamental contributions to the field ofanalytical geometryand was a pioneer in the investigations ofcathode raysthat led eventually to the discovery of theelectron.He also vastly extended the study ofLamécurves.

Biography

Early years

Plücker was born atElberfeld(now part ofWuppertal). After being educated atDüsseldorfand at the universities ofBonn,HeidelbergandBerlinhe went toParisin 1823, where he came under the influence of the great school of French geometers, whose founder,Gaspard Monge,had only recently died.

In 1825 he returned to Bonn, and in 1828 was made professor of mathematics.

In the same year he published the first volume of hisAnalytisch-geometrische Entwicklungen,which introduced the method of "abridged notation".

In 1831 he published the second volume, in which he clearly established on a firm and independent basisprojective duality.

Career

In 1836, Plücker was made professor of physics atUniversity of Bonn.In 1858, after a year of working with vacuum tubes of his Bonn colleagueHeinrich Geißler,he published his first classical researches on the action of the magnet on the electric discharge in rarefied gases. He found that the discharge caused a fluorescent glow to form on the glass walls of the vacuum tube, and that the glow could be made to shift by applying an electromagnet to the tube, thus creating a magnetic field.It was later shown that the glow was produced by cathode rays.

Plücker, first by himself and afterwards in conjunction withJohann Hittorf,made many important discoveries in the spectroscopy of gases. He was the first to use the vacuum tube with the capillary part now called aGeissler tube,by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipatedRobert Wilhelm BunsenandGustav Kirchhoffin announcing that the lines of the spectrum were characteristic of the chemical substance which emitted them, and in indicating the value of this discovery in chemical analysis. According to Hittorf, he was the first who saw the three lines of the hydrogen spectrum, which a few months after his death, were recognized in the spectrum of the solar protuberances.

In 1865, Plücker returned to the field of geometry and invented what was known asline geometryin the nineteenth century. Inprojective geometry,Plücker coordinatesrefer to a set ofhomogeneous co-ordinatesintroduced initially to embed the space of lines in projective space$\mathbf {P} ^{3}$as aquadricin$\mathbf {P} ^{5}$.The construction uses 2×2minor determinants,or equivalently the secondexterior powerof the underlyingvector spaceof dimension 4. It is now part of the theory ofGrassmannians$\mathbf {Gr} (k,V)$ ($k$-dimensional subspaces of an$n$-dimensional vector space$V$), to which the generalization of these co-ordinates to$k\times k$minors of the$n\times k$matrix of homogeneous coordinates, also known asPlücker coordinates,apply. The embedding of the Grassmannian$\mathbf {Gr} (k,V)$ into the projectivization$\mathbf {P} (\Lambda ^{k}(V))$of the$k$th exterior power of$V$ is known as thePlücker embedding.

Bibliography

• 1828:Analytisch-Geometrische EntwicklungenfromInternet Archive
• 1835:System der analytischen Geometrie, auf neue Betrachtungsweisen gegründet, und insbesondere eine ausführliche Theorie der Kurven dritter Ordnung enthaltend
• 1839:Theorie der algebraischen Curven, gegründet auf eine neue Behandlungsweise der analytischen Geometrie
• 1846:System der Geometrie des Raumes in neuer analytischer Behandlungsweise, insbesondere die Theorie der Flächen zweiter Ordnung und Classe enthaltend
• 1852:System der Geometrie des Raumes in neuer analytischer Behandlungsweise, insbesondere die Theorie der Flächen zweiter Ordnung und Classe enthaltend. Zweite wohlfeilere Auflage
• 1865:On a New Geometry of SpacePhilosophical Transactions of the Royal Society14: 53–8
• 1868: Neue Geometrie des Raumes gegründet auf die Betrachtung der geraden Linie als Raumelement. Erste Abtheilung. Leipzig.
• 1869: Neue Geometrie des Raumes gegründet auf die Betrachtung der geraden Linie als Raumelement. Zweite Abtheilung. Ed. F. Klein. Leipzig.
• 1895–1896:Gesammelte Wissenschaftliche Abhandlungen,Band 1 (vol. 1), Mathematische Abhandlungen (edited byArthur Moritz Schoenflies&Friedrich Pockels), Teubner 1895,Archive,Band 2 (vol. 2), Physikalische Abhandlungen (edited by Friedrich Pockels), 1896,Archive

Awards

Plücker was the recipient of theCopley Medalfrom theRoyal Societyin 1866.

See also

• Birkeland–Eyde process
• Duality (projective geometry)
• Grassmannian
• Ion pump
• Parameter space
• Timeline of low-temperature technology

Bibliography

• Born, Heinrich,Die Stadt Elberfeld. Festschrift zur Dreihundert-Feier 1910.J.H. Born, Elberfeld 1910
• Giermann, Heiko, Stammfolge der Familie Plücker, in: Deutsches Geschlechterbuch, 217. Bd, A. Starke Verlag, Limburg a.d.L. 2004
• Strutz, Edmund,Die Ahnentafeln der Elberfelder Bürgermeister und Stadtrichter 1708–1808.2. Auflage, Verlag Degener & Co., Neustadt an der Aisch 1963ISBN3-7686-4069-8
• Gustav Karsten(1888), "Plücker, Julius",Allgemeine Deutsche Biographie(in German), vol. 26, Leipzig: Duncker & Humblot, pp. 321–323

External links

• Julius Plückerat theMathematics Genealogy Project
• The Cathode Ray Tube site
• Weisstein, Eric Wolfgang(ed.)."Plücker, Julius (1801–1868)".ScienceWorld.
• O'Connor, John J.;Robertson, Edmund F.,"Julius Plücker",MacTutor History of Mathematics Archive,University of St Andrews
• Julius Plückerin theGerman National Librarycatalogue
• Julius Plücker in der philosophischen Fakultät der Universität Halle(PDF)
• Julius Plücker und die Stammfolge der Familie Plücker, Deutsches Geschlechterbuch, 217. Bd., A. Starke Verlag, Limburg a.d.L. 2004(Word)
• uni-bonn.de„Ein streitbarer Gelehrter im 19. Jahrhundert. Der Mathematiker Julius Plücker starb vor 140 Jahren. “Pressemitteilung der Universität Bonn vom 21. Mai 2008
• "Discussion of the general form for light waves"(English translation)