Home > Jakob Steiner

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 giving private lessons . 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 Jacobi's exertions, who was then professor at Königsberg, an honorary degree of that university; 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 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 such a rigour in his proofs that he has been considered the greatest geometrical genius since the time of Apollonius.

In his Systemalische Entwickelung der Abhundgigkeit 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 conicsIn mathematics, a conic section (or just conic is a curved locus of points, formed by intersecting a cone with a plane. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their propert and ruled quadricIn mathematics a quadric or quadric surface is any D-dimensional (hyper-)surface represented by a second-order equation in spatial variables (coordinates). If the space coordinates are , then the general quadric in such a space is defined by the algebraic 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 unfortunately only one volume appeared instead of the projected five, we see for the first time the principle of dualityDuality in the projective plane refers to the interchangeability between points and lines which preserves incidence properties. Notice that both points and lines can be represented (on a plane) by means of ordered pairs. A point is represented by the orde 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 ( 1833Events January 3 Britain seizes control of the Falkland Islands in the South Atlantic. June 6 U. President Andrew Jackson becomes the first President to ride a train. September 29 The infant Isabella II becomes Queen of Spain, under the regency of her mot), 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 circleSee The Circle for the distributed file storage system, and see Ring (diacritic) for the diacritic mark. In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius from a fixed point, called the centre . is given on the drawing-paper. He also wrote "Vorlesungen ber synthetische Geometrie", published posthumously at LeipzigLeipzig [ˈlaiptsɪç] ( Sorbian/Lusatian: Lipsk is the largest city in the federal state ( Bundesland) of Saxony in Germany. The name is derived from the Slavic word (see Sorbian) Lipsk (settlement where the linden trees stand). It is s by C. F. Geiser and H. Schroeter in 1867Events January 8 African-American men granted the right to vote in the District of Columbia January 11 Benito Juarez becomes Mexican president again January 30 Emperor Komei of Japan dies. Crown Prince Mutsuhito is expected to become the next Emperor of J; 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 Crelles Journal, the first volume of which contains his first four papers. The most important are those relating to algebrical 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 Krumniungsschwerpuncte ebener Curven, which contains numerous properties of pedals and roulettes, especially of their areas.

Steiner's papers were collected and published in two volumes (Gesammelte Werke, 1881-1882) by the Berlin Academy .

See also: Steiner surface.