Julius Plücker: Difference between revisions

Julius Plücker
Julius Plücker
	Julius Plücker
Born	16 June 1801; Elberfeld, Duchy of Berg, Holy Roman Empire
Died	22 May 1868 (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; Johann Hittorf ; Friedrich Lange

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Julius Plücker (16 June 1801 – 22 May 1868) was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves.

Biography

Early years

Plücker was born at Elberfeld (now part of Wuppertal). After being educated at Düsseldorf and at the universities of Bonn, Heidelberg and Berlin he went to Paris in 1823,^[2] 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.^[2]

In the same year he published the first volume of his Analytisch-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 basis projective duality.

Career

In 1836, Plücker was made professor of physics at University of Bonn. In 1858, after a year of working with vacuum tubes of his Bonn colleague Heinrich Geißler,^[3] 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.^[4] It was later shown that the glow was produced by cathode rays.

Plücker, first by himself and afterwards in conjunction with Johann 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 a Geissler tube, by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated Robert Wilhelm Bunsen and Gustav Kirchhoff in 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 as line geometry in the nineteenth century. In projective geometry, Plücker coordinates refer to a set of homogeneous co-ordinates introduced initially to embed the space of lines in projective space $\mathbf {P} ^{3}$ as a quadric in $\mathbf {P} ^{5}$ . The construction uses 2×2 minor determinants, or equivalently the second exterior power of the underlying vector space of dimension 4. It is now part of the theory of Grassmannians $\mathbf {Gr} (k,V)$ ( $k$ -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 as Plücker 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 the Plücker embedding.

Bibliography

1828: Analytisch-Geometrische Entwicklungen from Internet 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 Space Philosophical Transactions of the Royal Society 14: 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 by Arthur Moritz Schoenflies & Friedrich Pockels), Teubner 1895,^[5] Archive, Band 2 (vol. 2), Physikalische Abhandlungen (edited by Friedrich Pockels), 1896, Archive

Awards

Plücker was the recipient of the Copley Medal from the Royal Society in 1866.^[6]

References

^ ^a ^b "Julius Plücker – The Mathematics Genealogy Project". www.mathgenealogy.org.
^ ^a ^b Clebsch, Alfred (1872). "Zum Gedächtniss an Julius Plücker". Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. 16. doi:10.11588/heidok.00012662.
^ John Theodore Merz, A history of European thought in the nineteenth century (2). W. Blackwood and sons, 1912, pp. 189–190.
^ "Julius Plucker". chemed.chem.purdue.edu.
^ Scott, Charlotte Angas (1897). "Book Review: Julius Plückers gesammelte mathematische Abhandlungen". Bulletin of the American Mathematical Society. 4 (3): 121–126. doi:10.1090/S0002-9904-1897-00469-4. MR 1557565.
^ "Julius Plücker – Biography". Maths History.

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 1963 ISBN 3-7686-4069-8
Gustav Karsten (1888), "Plücker, Julius", Allgemeine Deutsche Biographie (in German), vol. 26, Leipzig: Duncker & Humblot, pp. 321–323

External links

Julius Plücker at the Mathematics 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 Plücker in the German National Library catalogue
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^{[permanent dead link‍]} „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)

[Genealogy-1] "Julius Plücker – The Mathematics Genealogy Project". www.mathgenealogy.org.

[Gedächtniss-2] Clebsch, Alfred (1872). "Zum Gedächtniss an Julius Plücker". Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. 16. doi:10.11588/heidok.00012662.

[3] John Theodore Merz, A history of European thought in the nineteenth century (2). W. Blackwood and sons, 1912, pp. 189–190.

[4] "Julius Plucker". chemed.chem.purdue.edu.

[5] Scott, Charlotte Angas (1897). "Book Review: Julius Plückers gesammelte mathematische Abhandlungen". Bulletin of the American Mathematical Society. 4 (3): 121–126. doi:10.1090/S0002-9904-1897-00469-4. MR 1557565.

[6] "Julius Plücker – Biography". Maths History.

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 5: / Line 5: @@
 | image        = Julius Plücker.jpg
 | caption      = Julius Plücker
-| birth_date   = {{birth date|1801|6|16|df=y}}{{citation needed|date=April 2015}}
+| birth_date   = {{birth date|1801|6|16|df=y}}
-| birth_place  = [[Elberfeld]], [[Duchy of Berg]], [[Holy Roman Empire]]{{citation needed|date=April 2015}}
+| birth_place  = [[Elberfeld]], [[Duchy of Berg]], [[Holy Roman Empire]]
-| death_date   = {{death date and age|1868|5|22|1801|6|16|df=y}}{{citation needed|date=April 2015}}
+| death_date   = {{death date and age|1868|5|22|1801|6|16|df=y}}
-| death_place  = [[Bonn]], [[Kingdom of Prussia]]{{citation needed|date=April 2015}}
+| death_place  = [[Bonn]], [[Kingdom of Prussia]]
-| nationality  = [[Germans|German]] {{citation needed|date=April 2015}} <!--Did Germany exist that time?-->
+| nationality  = [[Germans|German]]
 | field        = [[Mathematics]]<br>[[Physics]]
 | workplaces   = [[University of Bonn]]<br />[[University of Berlin]]<br />[[University of Halle]]
 | alma_mater   = [[University of Bonn]]<br />[[University of Heidelberg]]<br />[[University of Berlin]]<br />[[University of Paris]]<br />[[University of Marburg]]
-{{citation needed|date=April 2015}}
-| doctoral_advisor  = [[Christian Ludwig Gerling]]<ref>http://www.genealogy.ams.org/id.php?id=7402</ref>
+| doctoral_advisor  = [[Christian Ludwig Gerling]]<ref name = "Genealogy">{{Cite web|url=https://www.mathgenealogy.org/id.php?id=7402|title=Julius Plücker – The Mathematics Genealogy Project|website=www.mathgenealogy.org}}</ref>
-| doctoral_students = [[Felix Klein]]{{citation needed|date=April 2015}}<br />[[August Beer]]{{citation needed|date=April 2015}}
+| doctoral_students = [[Felix Klein]]<br />[[August Beer]]<br /> [[Johann Hittorf]] <br /> Friedrich Lange <ref name = "Genealogy></ref>
 | known_for     =  {{Plainlist|
+*[[Plücker's conoid]]
 *[[Plücker coordinates]]
-*[[Homogeneous coordinates]]
-*[[Plücker relations]]
 *[[Plücker embedding]]
-*[[Plücker formula]]}}
+*[[Plücker formula]]
+*[[Plücker matrix]]
+*[[Plücker relations]]
+*[[Plücker surface]]
+*[[Homogeneous coordinates]]
+}}
 | prizes        = [[Copley Medal]] (1866)
 }}
-'''Julius Plücker''' (16 June 1801 – 22 May 1868) was a German [[mathematician]] and [[physicist]]. He made fundamental contributions to the field of [[analytical geometry]] and was a pioneer in the investigations of [[cathode ray]]s that led eventually to the discovery of the [[electron]]. He also vastly extended the study of [[Gabriel Lamé|Lamé]] curves.
+'''Julius Plücker''' (16 June 1801 – 22 May 1868) was a German [[mathematician]] and [[physicist]]. He made fundamental contributions to the field of [[analytical geometry]] and was a pioneer in the investigations of [[cathode ray]]s that led eventually to the [[discovery of the electron]]. He also vastly extended the study of [[Lamé curve]]s.
 == Biography ==
-{{Unreferenced section|date=April 2015}}
 === Early years ===
-Plücker was born at [[Elberfeld]] (now part of [[Wuppertal]]). After being educated at [[Düsseldorf]] and at the universities of [[Bonn]], [[Heidelberg]] and Berlin he went to Paris in 1823, where he came under the influence of the great school of French geometers, whose founder, [[Gaspard Monge]], had only recently died.
+Plücker was born at [[Elberfeld]] (now part of [[Wuppertal]]). After being educated at [[Düsseldorf]] and at the universities of [[University of Bonn|Bonn]], [[University of Heidelberg|Heidelberg]] and [[University of Berlin|Berlin]] he went to [[University of Paris|Paris]] in 1823,<ref name = "Gedächtniss">{{cite journal|doi=10.11588/heidok.00012662|title=Zum Gedächtniss an Julius Plücker |year=1872|last1=Clebsch|first1=Alfred|journal=[[Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen]]|volume=16|doi-access=free}}</ref> 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 1825 he returned to Bonn, and in 1828 was made professor of mathematics.<ref name="Gedächtniss"></ref>
 In the same year he published the first volume of his ''Analytisch-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 basis [[projective duality]].
 === Career ===
-In 1836, Plücker was made professor of physics at [[University of Bonn]]. In 1858, after a year of working with vacuum tubes of his Bonn colleague [[Heinrich Geißler]],<ref>John Theodore Merz, ''A history of European thought in the nineteenth century'' (2). W. Blackwood and sons, 1912, pp. 189–190.</ref> 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.<ref>http://chemed.chem.purdue.edu/genchem/history/plucker.html</ref> It was later shown that the glow was produced by cathode rays.
+In 1836, Plücker was made professor of physics at [[University of Bonn]]. In 1858, after a year of working with vacuum tubes of his Bonn colleague [[Heinrich Geißler]],<ref>John Theodore Merz, ''A history of European thought in the nineteenth century'' (2). W. Blackwood and sons, 1912, pp. 189–190.</ref> 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.<ref>{{Cite web|url=http://chemed.chem.purdue.edu/genchem/history/plucker.html|title=Julius Plucker|website=chemed.chem.purdue.edu}}</ref> It was later shown that the glow was produced by cathode rays.
 Plücker, first by himself and afterwards in conjunction with [[Johann Wilhelm Hittorf|Johann 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 a [[Geissler tube]], by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated [[Robert Wilhelm Bunsen]] and [[Gustav Kirchhoff]] in 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 as ''[[line geometry]]'' in the nineteenth century. In [[projective geometry]], [[Plücker coordinates]] refer to a set of [[homogeneous co-ordinates]] introduced initially to embed the space of lines in projective space <math>\mathbf{P}^3</math> as the [[quadric (algebraic geometry)|quadric]] in <math>\mathbf{P}^5</math>. The construction uses 2×2 [[minor determinant]]s, or equivalently the second [[exterior power]] of the underlying vector space of dimension 4. It is now part of the theory of [[Grassmannian]]s, to which these co-ordinates apply in generality (''k''-dimensional subspaces of ''n''-dimensional space).
+In 1865, Plücker returned to the field of geometry and invented what was known as ''[[line geometry]]'' in the nineteenth century. In [[projective geometry]], [[Plücker coordinates]] refer to a set of [[homogeneous co-ordinates]] introduced initially to embed the space of lines in projective space <math>\mathbf{P}^3</math> as a [[quadric (algebraic geometry)|quadric]] in <math>\mathbf{P}^5</math>. The construction uses 2×2 [[minor determinant]]s, or equivalently the second [[exterior power]] of the underlying [[vector space]] of dimension 4. It is now part of the theory of [[Grassmannian]]s <math>\mathbf{Gr}(k, V)</math>
+(<math> k </math>-dimensional subspaces of an <math>n</math>-dimensional vector space <math> V</math>), to which the generalization of these co-ordinates to <math>k \times k </math> minors of the <math> n \times k </math> matrix of homogeneous coordinates, also known as [[Plücker coordinates]], apply. The embedding of the Grassmannian <math>\mathbf{Gr}(k, V)</math>
+into the projectivization <math> \mathbf{P}(\Lambda^k(V))</math> of the <math>k</math>th exterior power of <math>V</math>
+is known as the [[Plucker embedding|Plücker embedding]].
 ==Bibliography==
@@ Line 53: / Line 59: @@
 * 1852: [https://archive.org/details/bub_gb_7DBaxlXVU-gC ''System der Geometrie des Raumes in neuer analytischer Behandlungsweise, insbesondere die Theorie der Flächen zweiter Ordnung und Classe enthaltend. Zweite wohlfeilere Auflage'']
 * 1865: [https://archive.org/details/philtrans04968378 On a New Geometry of Space] ''Philosophical Transactions of the Royal Society'' 14: 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 by [[Arthur Moritz Schoenflies]] &  [[Friedrich Pockels]]), Teubner 1895,<ref>{{cite journal|doi=10.1090/S0002-9904-1897-00469-4|title=Book Review: ''Julius Plückers gesammelte mathematische Abhandlungen''|year=1897|last1=Scott|first1=Charlotte Angas|author-link=Charlotte Scott|journal=[[Bulletin of the American Mathematical Society]]|volume=4|issue=3|pages=121–126|mr=1557565|doi-access=free}}</ref> [https://archive.org/details/juliusplckersge02pockgoog Archive], Band 2 (vol. 2), Physikalische Abhandlungen (edited by Friedrich Pockels), 1896, [https://archive.org/details/juliusplckersge00pockgoog Archive]
 ==Awards==
-Plücker was the recipient of the [[Copley Medal]] from the [[Royal Society]] in 1866.<ref>http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Plucker.html</ref>
+Plücker was the recipient of the [[Copley Medal]] from the [[Royal Society]] in 1866.<ref>{{Cite web|url=https://mathshistory.st-andrews.ac.uk/Biographies/Plucker/|title=Julius Plücker – Biography|website=Maths History}}</ref>
 == See also ==
-*[[Plücker's conoid]]
+*[[Birkeland–Eyde process]]
+*[[Duality (projective geometry)]]
-*[[Plücker coordinates]]
-*[[Plücker embedding]]
+*[[Grassmannian]]
+*[[Ion pump (physics)|Ion pump]]
-*[[Plücker formula]]
-*[[Plücker surface]]
+*[[Parameter space]]
-*[[Plücker matrix]]
 *[[Timeline of low-temperature technology]]
@@ Line 72: / Line 80: @@
 * 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 1963 {{isbn|3-7686-4069-8}}
+* Strutz, Edmund, ''Die Ahnentafeln der Elberfelder Bürgermeister und Stadtrichter 1708–1808''. 2. Auflage, Verlag Degener & Co., Neustadt an der Aisch 1963 {{isbn|3-7686-4069-8}}
 * {{Cite ADB|26|321|323|Plücker, Julius|[[Gustav Karsten]]|ADB:Plücker, Julius}}
 == External links ==
-{{Commons | Julius Plücker}}
+{{Commons }}
 * {{MathGenealogy|id=7402}}
 * [http://www.crtsite.com/page7.html The Cathode Ray Tube site]
-* {{ScienceWorldBiography | urlname=Pluecker | title=Plücker, Julius (1801-1868)}}
+* {{ScienceWorldBiography | urlname=Pluecker | title=Plücker, Julius (1801–1868)}}
 * {{MacTutor Biography | id=Plucker}}
 * {{DNB portal|11879258X|TYP=}}
@@ Line 94: / Line 102: @@
 [[Category:1801 births]]
 [[Category:1868 deaths]]
-[[Category:19th-century German scientists]]
 [[Category:19th-century German mathematicians]]
-[[Category:German physicists]]
+[[Category:19th-century German physicists]]
 [[Category:Recipients of the Copley Medal]]
 [[Category:People from Elberfeld]]
 [[Category:People from the Rhine Province]]
-[[Category:University of Bonn faculty]]
+[[Category:Academic staff of the University of Bonn]]
-[[Category:Foreign Members of the Royal Society]]
+[[Category:Foreign members of the Royal Society]]
+[[Category:Scientists from Wuppertal]]
+[[Category:University of Paris alumni]]
+[[Category:Mathematicians from the Kingdom of Prussia]]

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