Jakob steiner. Life History of Jakob Steiner Essay Example 2022-10-21
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Jakob Steiner was a Swiss mathematician who made significant contributions to geometry in the 19th century. He was born in 1796 in the village of Utzenstorf, Switzerland and showed an early aptitude for math and science. He studied at the University of Bern and later taught at the Gymnasium in Bern, where he became well-known for his mathematical abilities.
One of Steiner's most famous contributions to geometry was his work on the theory of conic sections. He developed a new method for constructing the tangents to a conic section, which became known as Steiner's construction. He also made significant contributions to the study of higher-dimensional geometry and was the first to prove that there are exactly five regular polyhedra in four dimensions.
In addition to his work in geometry, Steiner also made contributions to other areas of mathematics, including algebra and number theory. He was a member of the Swiss Academy of Sciences and was highly respected by his peers for his mathematical skills and insights.
Steiner's contributions to geometry were recognized and celebrated throughout his lifetime, and he received numerous awards and accolades for his work. Despite his many achievements, however, he remained humble and dedicated to his work, always striving to improve upon his existing knowledge and understanding of math.
In conclusion, Jakob Steiner was a brilliant mathematician who made significant contributions to the field of geometry and other areas of mathematics. His work laid the foundation for many important developments in these fields and he remains an important figure in the history of mathematics.
Jacob Steiner
Propositions 49â53 deal with the production of projective figures in space. It was likewise by means of an inversion that Steiner found and proved his famous theorem on series of circles § IV, no. In reverse order, they are Malfatti's problem, Apollonius' problem, Cramer-Castillon problem, and Steiner's problem. Following from his original work, Steiner derived other mathematical theorems and relationships. He sought to assign each its special position in relation to the others, to bring order to chaos, to interlock all parts according to nature, and to assemble them into well-defined groups. The latter belongs to triangle geometry and deserves to be better known: Suppose that we are given three straight lines l, m, n and three points P, Q, R in a plane. This connection and transition is the real source of all the remaining individual propositions of geometry.
Lectures, originally published in 1867 after his death by his former student Heinrich Schröter or Schröder. Within a year and a half he was teaching math to other students and had adopted an innovative approach to his subject. Violins and Violin Makers: Biographical Dictionary of the Great Italian Artistes, Their Followers and Imitators, to the Present Time. A Dedicated Educator Through the efforts of Jacobi as well as other noted German intellectuals, on October 8, 1834, the 38-year-old mathematician was honored by the University of Berlin, which established a chair of geometry for him. Despite his parents' objections, in 1814 the 18-year-old farmer's son left home and traveled to Yverdon, where educational reformer Johann Heinrich Pestalozzi 1746-1827 had established a school.
Despite being a mathematical genius, in other ways Steiner was a difficult person. NOTES Archiv der Mathematik und Physik, 3rd ser. Although he was dismissed within a few months due to his unconventional teaching methods, the resourceful young man managed to replace this job with work as a tutor, and by November of 1822 Steiner was enrolled at the University of Berlin. 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. Born to a farm family near Bern, Switzerland, at first his opportunities for education were meager.
BiografĂa de Jakob Steiner (Su vida, historia, bio resumida)
He never married, but dedicated much of his adult life to his students. Like Poncelet, Steiner believed that geometry was a tool that encouraged creative thinking while algebra merely reiterated existing numerical complexities. Bibliotheca mathematica, 3rd ser. Draw a triangle ABC in such a way that vertices A, B, C lie on l, m, n and sides BC, CA, AB pass through P, Q, R. Properties of figures the very existence of which one previously had to be convinced through ingenious demonstrations and which, when found, stood as something marvellous, are now revealed as necessary consequences of the common properties of these newly discovered basic elements, and the former are established a priori by the latter.
Abel as in abelian groups , A. This paper is important as being the first published systematic account of the theory of the power of a point with respect to a circle, and the points of similitude of circles. Despite the bad atmosphere, Steiner managed to carry out some outstanding mathematical research while teaching at the Technical School. One of the simplest follows. Three years later, he moved to Berlin and continued teaching. The post had been specially created for him by Alexander and Wilhelm von Humboldt; he held it until his death. In a given triangle ABC draw three circles a, b, and c that are tangent to each other and such that each is tangent to two sides of the triangle Figure 1.
Ostern 1899, Program no. Crelle, the Journal fĂŒr die reine und angewandte Mathematik Journal for Pure and Complex Mathematics. Anna and Niklaus were married on 28 January 1780 and they had eight children. Not having passed any academic examinations, he was now obliged to do so in order to obtain a teaching license. Perhaps, understandably, Zimmermann wanted Steiner to teach his courses using a textbook written by Zimmermann himself. Or, as Pappus expressed it: the perpendicular m 1 p 1 plus the diameter of the corresponding circle m 1 is to that diameter as the perpendicular m 2 P 2 is to the diameter of the corresponding circle m 2âthat is,. Let A and B be two points that bisect the perimeter.
Also at this time he became interested in mechanics and he wrote three unpublished manuscripts on the topic in 1821, 1824 and 1825. His collected writings, Gesammelte Werke, were published in two volumes in 1881 and 1882. His methodology, which has since become a foundation of elementary educational theory, takes into account the unique needs and talents of each student; traditional classroom repetition and memorization are replaced by hands-on learning and the resulting development of critical-thinking skills. He was awarded an honorary doctorate by the University of Königsberg on 20 April 1833 on the recommendation of 5 June 1834. Steiner was one of the greatest of all geometers. Three years later, in the early spring of 1821, he followed the suggestion of a friend and moved to the Prussian capital city of Berlin in hopes of finding a teaching post and then enrolling at the city's prestigious university.
This connection and transition is the real source of all the remaining individual propositions of geometry. He attended lectures at the Universities of Heidelberg on combinatorial analysis, differential and integral calculus and algebra. During an austere childhood in a poor and unlettered family he showed extr⊠Archimedes , Archimedes Archimedes b. Gesammelte Abhandlungen Berlin, 1932 , 151. There his extraordinary geometric intuition was discovered.
Dedicating himself to the education of the poor, he used his school to put a number of his educational theories to the test, in 1805 opening a University Career in Germany In the fall of 1818 Steiner left his native Switzerland and moved to Germany to attend the University of Heidelberg, where he fell into the company of other mathematicians, such as Norwegian-born The lack of a formal, structured education came back to haunt Steiner in Berlin. One of the greatest geometers in history was the Swiss mathematician Jakob Steiner. Dörrie, Heinrich, One Hundred Great Problems of Elementary Mathematics, Their History and Solution, translated from the German by David Antin, Dover, 1965. Gesammelte Werke, I, 133. Examination of his posthumous papers shows that he knew of the principle of inversion and that he used it in finding and proving the above and other theorems. See also Jakob Steiner was born on March 18, 1796, in Utzenstorf, Switzerland.
Just as related theorems in a single branch of mathematics grow out of one another in distinct classes, so, I believed, do the branches of mathematics itself. 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 spent the winter of 1854- 55 in Paris and during his stay there was elected to the He was one of the greatest contributors to Die geometrischen Konstructionen ausgefuhrt mittelst der geraden Linie and eines festen Kreises Geometric construction executed by means of the straight line and a circle 1833. Ueber die FlÀchen dritten Grades. At Easter 1821 he left Heidelberg and travelled to Berlin, where again he supported himself with a very modest income from tutoring. . From these almost all other properties of the conics can be developed in a single, comprehensive framework and in a surprisingly simple and clear manner.
