Julius Plücker (16 June 1801 – 22 May 1868) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
. He made fundamental contributions to the field of
analytical geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineerin ...
and was a pioneer in the investigations of
cathode ray
Cathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to ele ...
s that led eventually to the discovery of the
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
. He also vastly extended the study of
Lamé curves.
Biography
Early years
Plücker was born at
Elberfeld
Elberfeld is a municipal subdivision of the German city of Wuppertal; it was an independent town until 1929.
History
The first official mentioning of the geographic area on the banks of today's Wupper River as "''elverfelde''" was in a docu ...
(now part of
Wuppertal
Wuppertal (; "''Wupper Dale''") is, with a population of approximately 355,000, the seventh-largest city in North Rhine-Westphalia as well as the 17th-largest city of Germany. It was founded in 1929 by the merger of the cities and to ...
). After being educated at
Düsseldorf
Düsseldorf ( , , ; often in English sources; Low Franconian and Ripuarian: ''Düsseldörp'' ; archaic nl, Dusseldorp ) is the capital city of North Rhine-Westphalia, the most populous state of Germany. It is the second-largest city in th ...
and at the universities of
Bonn
The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ruhr r ...
,
Heidelberg
Heidelberg (; Palatine German language, Palatine German: ''Heidlberg'') is a city in the States of Germany, German state of Baden-Württemberg, situated on the river Neckar in south-west Germany. As of the 2016 census, its population was 159,914 ...
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
Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. Durin ...
, 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 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
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of du ...
.
Career
In 1836, Plücker was made professor of physics at
University of Bonn
The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...
. In 1858, after a year of working with vacuum tubes of his Bonn colleague
Heinrich Geißler
Johann Heinrich Wilhelm Geißler (26 May 1814 in Igelshieb – 24 January 1879) was a skilled glassblower and physicist, famous for his invention of the Geissler tube, made of glass and used as a low pressure gas-discharge tube.
Geissler desc ...
, 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 with
Johann Hittorf
Johann Wilhelm Hittorf (27 March 1824 – 28 November 1914) was a German physicist who was born in Bonn and died in Münster, Germany.
Hittorf was the first to compute the electricity-carrying capacity of charged atoms and molecules (ions), an ...
, 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
A Geissler tube is an early gas discharge tube used to demonstrate the principles of electrical glow discharge, similar to modern neon lighting. The tube was invented by the German physicist and glassblower Heinrich Geissler in 1857. It consist ...
, by means of which the luminous intensity of feeble electric discharges was raised sufficiently to allow of spectroscopic investigation. He anticipated
Robert Wilhelm Bunsen
Robert Wilhelm Eberhard Bunsen (;
30 March 1811
– 16 August 1899) was a German chemist. He investigated emission spectra of heated elements, and discovered caesium (in 1860) and rubidium (in 1861) with the physicist Gustav Kirchhoff. The Buns ...
and
Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects.
He coine ...
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 geometry, line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.
Lines in the plane
There are several possible ways to specify the position o ...
'' in the nineteenth century. In
projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...
,
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to- ...
refer to a set of
homogeneous co-ordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. T ...
introduced initially to embed the space of lines in projective space
as a
quadric
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is de ...
in
. The construction uses 2×2
minor determinant
In linear algebra, a minor of a matrix (mathematics), matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square ...
s, or equivalently the second
exterior power
In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is a ...
of the underlying vector space of dimension 4. It is now part of the theory of
Grassmannian
In mathematics, the Grassmannian is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the ...
s
(
-dimensional subspaces of an
-dimensional vector space
), to which the generalization of these co-ordinates to
minors of the
matrix of homogeneous coordinates, also known as
Plücker coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to- ...
, apply. The embedding of the Grassmannian
into the projectivization
of the
th exterior power of
is known as the
Plücker embedding In mathematics, the Plücker map embeds the Grassmannian \mathbf(k,V), whose elements are ''k''-dimensional subspaces of an ''n''-dimensional vector space ''V'', in a projective space, thereby realizing it as an algebraic variety.
More precisely ...
.
Bibliography
* 1828
''Analytisch-Geometrische Entwicklungen''from
Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
* 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
Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
Schoenflies ...
&
Friedrich Pockels
Friedrich Carl Alwin Pockels (18 June 1865 – 29 August 1913) was a German physicist. He was born in Italy to Captain Theodore Pockels and Alwine Becker. He obtained a doctorate from the University of Göttingen in 1888, and from 1900 to 1913 h ...
), Teubner 1895
Archive Band 2 (vol. 2), Physikalische Abhandlungen (edited by Friedrich Pockels), 1896
Archive
Awards
Plücker was the recipient of the
Copley Medal
The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...
from the
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
in 1866.
See also
*
Birkeland–Eyde process
The Birkeland–Eyde process was one of the competing industrial processes in the beginning of nitrogen-based fertilizer production. It is a multi-step nitrogen fixation reaction that uses electrical arcs to react atmospheric nitrogen (N2) with ox ...
*
Duality (projective geometry)
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of dua ...
*
Grassmannian
In mathematics, the Grassmannian is a space that parameterizes all -Dimension, dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the ...
*
Ion pump
An ion pump (also referred to as a sputter ion pump) is a type of vacuum pump which operates by sputtering a metal getter. Under ideal conditions, ion pumps are capable of reaching pressures as low as 10−11 mbar. An ion pump first ionizes ga ...
*
Parameter space The parameter space is the space of possible parameter values that define a particular mathematical model, often a subset of finite-dimensional Euclidean space. Often the parameters are inputs of a function, in which case the technical term for the ...
*
Timeline of low-temperature technology
The following is a timeline of low-temperature technology and cryogenic technology (refrigeration down to –273.15 °C, –459.67 °F or 0 K). It also lists important milestones in thermometry, thermodynamics, statistical physics and ca ...
References
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
*
External links
*
The Cathode Ray Tube site*
*
*
''Julius Plücker in der philosophischen Fakultät der Universität Halle''(
PDF
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ...
)
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)
{{DEFAULTSORT:Plucker, Julius
1801 births
1868 deaths
19th-century German mathematicians
19th-century German physicists
Recipients of the Copley Medal
People from Elberfeld
People from the Rhine Province
University of Bonn faculty
Foreign Members of the Royal Society
Scientists from Wuppertal