Jakob Steiner
Jakob Steiner (
18 March ,
1796 –
April 1,
1863) was a
Swiss mathematician.
He was born in the village of
Utzendorf,
Canton of Bern. At eighteen he became a pupil of
Heinrich Pestalozzi, and afterwards studied at
Heidelberg. Thence he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with
A. L. Crelle, who, encouraged by his ability and by that of
N. H. Abel, then also staying at Berlin, founded his famous
Journal (1826).
After Steiner's publication (1832) of his
Systematische Entwickelungen he received, through
C. G. J. Jacobi, who was then professor at
Königsberg University, an honorary degree there; and through the influence of
G. J. Jacobi and of the brothers Alexander and
Wilhelm von Humboldt a new chair of geometry was founded for him at
Berlin (1834). This he occupied till his death, which took place in Bern on the 1st of April
1863.
Steiner's mathematical work was confined to
geometry. This he treated synthetically, to the total exclusion of analysis, which he hated, and he is said to have considered it a disgrace to
synthetical geometry if equal or higher results were obtained by
analytical geometry methods. In his own field he surpassed all his contemporaries. His investigations are distinguished by their great generality, by the fertility of his resources, and by the
rigour in his proofs. He has been considered the greatest pure geometer genius since
Apollonius of Perga.
In his
Systematische Entwickelung der Abhängigkeit geometrischer Gestalten von einander he laid the foundation of modern
synthetic geometry. He introduces what are now called the geometrical forms (the
row,
flat pencil etc.), and establishes between their elements a one-one correspondence, or, as he calls it, makes them
projective. He next gives by aid of these projective rows and pencils a new generation of
conics and ruled
quadric surfaces, which leads quicker and more directly than former methods into the inner nature of conics and reveals to us the organic connection of their innumerable properties and mysteries. In this work also, of which only one volume appeared instead of the projected five, we see for the first time the principle of
duality introduced from the very beginning as an immediate outflow of the most fundamental properties of the plane, the line and the point.
In a second little volume,
Die geometrischen Constructionen ausgeführt mittels der geraden Linie und eines festen Kreises (
1833), republished in 1895 by Ottingen, he shows, what had been already suggested by
J. V. Poncelet, how all problems of the second order can be solved by aid of the straight edge alone without the use of compasses, as soon as one
circle is given on the drawing-paper. He also wrote
"Vorlesungen über synthetische Geometrie", published posthumously at
Leipzig by C. F. Geiser and H. Schroeter in
1867; a third edition by
R. Sturm was published in 1887-1898.
The rest of Steiner's writings are found in numerous papers mostly published in
Crelle's Journal, the first volume of which contains his first four papers. The most important are those relating to
algebraic curves and surfaces, especially the short paper
Allgemeine Eigenschaften algebraischer Curven. This contains only results, and there is no indication of the method by which they were obtained, so that, according to
L. O. Hosse, they are, like
Fermat's theorems, riddles to the present and future generations. Eminent analysts succeeded in proving some of the theorems, but it was reserved to
L. Cremona to prove them all, and that by a uniform synthetic method, in his book on algebraic curves.
Other important investigations relate to
maxima and
minima. Starting from simple elementary propositions, Steiner advances to the solution of problems which analytically require the
calculus of variations, but which at the time altogether surpassed the powers of that calculus. Connected with this is the paper
Vom Krümmungsschwerpuncte ebener Curven, which contains numerous properties of
pedals and
roulettes, especially of their areas.
He was described by Thomas Hirst as follows: ::
"He is a middle-aged man, of pretty stout proportions, has a long intellectual face, with beard and moustache and a fine prominent forehead, hair dark rather inclining to turn grey. The first thing that strikes you on his face is a dash of care and anxiety, almost pain, as if arising from physical suffering - he has rheumatism. He never prepares his lectures beforehand. He thus often stumbles or fails to prove what he wishes at the moment, and at every such failure he is sure to make some characteristic remark."Steiner died April 1, 1863 in Bern, Switzerland.
*
Steiner surface*
Poncelet-Steiner theorem*
Parallel axes rule*
Steiner, J. (1796-1863)
