Steiner's Theorem Steiner'sTheorem by June Jones Steiner's Theorem, named for Jakob Steiner 1796 - 1863 , isincluded in most high school geometry books but rarely by name. In contrast, geometry developed from ancient man's desire to measure the earth, a goal impossible to accomplish except by abstract means. Born to a farm family near Bern, Switzerland, at first his opportunities for education were meager. Three years later, he moved to Berlin and continued teaching. His father had been an officer in and spent 4 years as a in. This paper was the first of 62 papers which Steiner published in 's Journal. He was a visiting Associate Professor to the.
He was appointed to a new extraordinary professorship of geometry at the University of Berlin on 8 October 1834. These articles combine with his book-length works Systematische Entwicklung der Abhangigkeit geometrischer Gestalten voneinander 1832 , the two-volume Vorlesungen üuber synthetische Geometrie 1867 , and Allgemeine Theorie über das Berühren und Schneiden der Kreise und der Kugeln 1931 to encompass Steiner's foundational work in the area of what has since become the discipline of projective, or pure geometry. Online Jakob Steiner 1796-1863 Geometer, February 12, 2003. Steiner died in Bern, Switzerland, on April 1, 1863. The official reason was that his teaching was receiving criticism but the real reason was clearly his desire to use the methods he thought best rather than those required by the director, Dr Zimmermann.
His problem was not in mathematics but in the other subjects which were examined such as history and literature. 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. Although he left Yverdon at age 22, he continued to draw on Pestalozzi's approach. In discovering the organism through which the most varied phenomena of space are linked, he not only furthered the development of a geometric synthesis; he also provided a model of a complete method and execution for all other branches of mathematics. Since we moved P inside the circle, we should give a formal proof for the newfigure. Order replaces chaos: and one sees how all the parts mesh naturally, arrange themselves in the most beautiful order, and form well-defined groups.
The principle underlying Steiner's projective geometry is the principle of duality, an algebraic concept that holds that if A equals B, then what holds for A holds as well for B. Steiner, who was a firm believer in Pestalozzi's methods of teaching, used those methods in the classroom. He was known for both the startling nature of his lectures and the originality of his research, and influenced many of his students, including the noted mathematician Georg Friedrich Bernhard Riemann. Following from his original work, Steiner derived other mathematical theorems and relationships. Steiner reasoned that what held for complex numbers should hold also for complex shapes, and through his work he proved that if two geometric operations are interchangeable or dual, then whatever results are true for one are also true for the other. In this manner one obtains, simultaneously, the elements from which nature starts when, with the greatest possible economy and in the simplest way, it endows the figures with infinitely many properties. The Steiner surface contains an infinity of conic sections; the Steiner theorem states that the points of intersection of corresponding lines of two sets of geometric objects form a conic section.
He later studied in Heidelberg and Berlin, Germany. At the age of 18, however, Steiner left home to pursue his education at the Pestalozzi School in Yverdon, Switzerland. At Easter 1821 he left Heidelberg and travelled to Berlin, where again he supported himself with a very modest income from tutoring. Much of the material had already appeared in Steiner's papers over the preceding six years. One of the greatest geometers in history was the Swiss mathematician Jakob Steiner. His collected writings, Gesammelte Werke, were published in two volumes in 1881 and 1882.
He had no formal teaching qualifications so he decided that he needed to sit the necessary examinations to allow him to become a mathematics master in a. If, for any reason, you do not wish us to retain your details for these purposes then please let us know either when you first contact us or at any time thereafter. Perhaps his three greatest theorems were the Poncelet-Steiner Theorem, Double-Element Theorem, and the Isoperimetric Theorem. It is said that he first learned to write at the age of fourteen. Inspired by Steiner, Riemann 1826-1866 went on to become professor of mathematics at Göttingen and developed the system of elliptical space that Albert Einstein would one day draw on in his formulation of the Theory of Relativity.
In a short paper of fundamental importance written in 1848 entitled Allgemeine Eigenschaften algebraischer Curven he discussed polar curves of a point with respect to a given curve. Jakob Steiner Essay Jakob Steiner Born 1796 in Switzerland this mathematician had hopes of renovating the classic methods of geometry. Spinoza supplied no diagram, but, it seems clear that a diagram like figure 4 is what he had in mind. In 1818, Steiner moved to Heidelberg, Germany, where he gave private instruction in mathematics. At the age of 14 he learned to write, and the mastery of this skill Steiner saw as a way to escape the harsh life of a farmer. Personal details supplied via contacting us will only be used for queries, future dealings or to notify you of future news, development or offers. There his extraordinary geometric intuition was discovered.
It was through Jacobi's efforts, while a professor at the University of Königsberg, that this university conferred on Steiner an honorary Ph. Today these ellipses are called the 'Steiner ellipses'. Like Poncelet, Steiner believed that geometry was a tool that encouraged creative thinking while algebra merely reiterated existing numerical complexities. Algebra is the area of mathematics that uses letters or other symbols to describe the properties and relationships among complex numbers and other abstract entities. His investigations are distinguished by their great generality, by the fertility of his resources, and by the rigour in his proofs. However, to some it may be important to provide a formal proof. The classical construction of the Steiner point link below , however, does not depend on the Steiner ellipse.
He was a fascinating figure in the history of mathematics not only because of the depth and originality of his geometrical work but also because of his unique educational background. . Following from his original work, Steiner derived other mathematical theorems and relationships. In his will Steiner bequeathed a third of his fortune to the Berlin Academy to establish the Steiner Prize. Again through the influence of Jacobi, an honorary doctorate from the University of Königsberg was conferred upon Steiner in 1833, and the following year he was elected a fellow of the Prussian Academy of Science. In 1853, Steiner published a two pages article in Crelle's Journal on what nowadays is called Steiner systems, a basic kind of block design. Here he became acquainted with A.
Steiner also extrapolated the work of his colleague, French geometer Jean Poncelet 1788-1837 , a military engineer and professor of mechanics at the University of Paris. Despite the bad atmosphere, Steiner managed to carry out some outstanding mathematical research while teaching at the Technical School. Jakob Steiner was born on March 18, 1796, in Utzenstorf, Switzerland. Shown above is the title page of his Lectures, originally published in 1867 after his death by his former student Heinrich Schröter or Schröder. Steiner remained an extraordinary professor at the university until his death 29 years later. In 1825 Steiner was appointed as an assistant master at the Technical School of Berlin. Steiner disliked algebra and analysis and believed that calculation replaces thinking while geometry stimulates thinking.