Editing Julius Plücker (section)

=== 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>{{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 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]].