Search Results for Steiner


Biographies

  1. Jakob Steiner (1796-1863)
    • Jakob Steiner .
    • Jakob Steiner's parents were Anna Barbara Weber (1757-1832) and Niklaus Steiner (1752-1826).
    • Pestalozzi ran his innovative school in the town from 1805 to 1825 and Steiner entered in the spring of 1814.
    • The fact that Steiner was unable to pay anything towards his education at the school was not a problem, for Pestalozzi wanted to try out his educational methods on the poor.
    • Pestalozzi's school had a very significant effect on Steiner's attitude both to the teaching of mathematics and also to his philosophy when undertaking research in mathematics.
    • In the autumn of 1818, Steiner left Yverdom and travelled to Heidelberg where he earned his living giving private mathematics lessons.
    • Steiner's time as a mathematics teacher at the Werder Gymnasium proved a difficult one.
    • Perhaps, understandably, Zimmermann wanted Steiner to teach his courses using a textbook written by Zimmermann himself.
    • Steiner, who was a firm believer in Pestalozzi's methods of teaching, used those methods in the classroom.
    • Zimmermann claimed that these were only suitable for elementary courses, and Steiner was dismissed in the autumn of 1822.
    • Carl Jacobi, although eight years younger than Steiner, was a student at the University of Berlin at this time and soon Steiner and Jacobi became friends.
    • In 1825 Steiner was appointed as an assistant master at the Technical School of Berlin.
    • The type of difficulties that Steiner had experienced at the Werder Gymnasium again arose at the Technical School.
    • Kloden, almost certainly correctly, believed that Steiner was not giving him the respect that he deserved.
    • He retaliated in a severe manner, making unreasonable demands of Steiner that [',' J J Burckhardt, Biography in Dictionary of Scientific Biography (New York 1970-1990).','1]:- .
    • Despite the bad atmosphere, Steiner managed to carry out some outstanding mathematical research while teaching at the Technical School.
    • We have already mentions that Steiner became friendly with Jacobi, but he also became friendly with other influential mathematicians in Berlin.
    • Steiner became an early contributor to Crelle's Journal, the Journal fur die reine und angewandte Mathematik, which was the first journal devoted entirely to mathematics founded.
    • The first volume of the journal appeared in 1826 and contains Steiner's first long work, Einige geometrische Betrachtungen Ⓣ.
    • It is also important for Steiner's use of the principle of inversion in many of the proofs.
    • This paper was the first of 62 papers which Steiner published in Crelle's Journal.
    • In 1832 Steiner published his first book Systematische Entwicklung der Abhangigkeit geometrischer Gestalten voneinander Ⓣ.
    • Much of the material had already appeared in Steiner's papers over the preceding six years.
    • The Preface of this book gives an interesting view of Steiner's approach to mathematics in general and the geometric material of book in particular:- .
    • Soon Steiner was being honoured for his remarkable achievements.
    • He was in Rome in 1844 and on this visit he spent his time investigating a fourth order surface of the third class now called the 'Roman surface' or 'Steiner surface'.
    • He discovered the 'Steiner surface' which has a double infinity of conic sections on it.
    • The 'Steiner theorem' states that the two pencils by which a conic is projected from two of its points are projectively related.
    • Another famous result is the 'Poncelet-Steiner theorem' which shows that only one given circle and a straight edge are required for Euclidean constructions.
    • The proof, essentially as given by Steiner, is reproduced in [',' H Dorrie, One Hundred Great Problems of Elementary Mathematics, Their History and Solution (Dover, 1965).','3].
    • For example he considered the problem: Of all ellipses that can be circumscribed about (inscribed in) a given triangle, which one has the smallest (largest) area? Today these ellipses are called the 'Steiner ellipses'.
    • He also introduced Steiner curves, discussed tangents at points of inflection, double tangents, cusps and double points.
    • This wealth of material is presented, however, without any indication of the proofs which Steiner had found.
    • Steiner disliked algebra and analysis and believed that calculation replaces thinking while geometry stimulates thinking.
    • Jacobi wrote of his friend Steiner:- .
    • Starting from a few spatial properties Steiner attempted, by means of simple schema, to attain a comprehensive view of the multitude of geometric theorems that had been rent asunder.
    • Despite being a mathematical genius, in other ways Steiner was a difficult person.
    • Students and contemporaries wrote of the brilliance of Steiner's geometric research and of the fiery temperament he displayed in leading others into the new territory he had discovered.
    • The last ten years of Steiner's life were increasingly difficult through illness.
    • Steiner never married and, perhaps as a consequence, left a fortune on his death.
    • One third of this fortune went to the Berlin Academy to found the Steiner Prize.
    • A Poster of Jakob Steiner .
    • Butzberger's Work on Steiner .
    • https://www-history.mcs.st-andrews.ac.uk/Biographies/Steiner.html .

  2. Georg Sidler (1831-1907)
    • There he attended lectures on a range of mathematical topics by Dirichlet, on theoretical astronomy by Encke, on geodesy by Bremiker, on mathematical physics by Clausius and on geometry by Steiner.
    • Sidler often went for a walk with Steiner; the two mathematicians stayed in touch for the rest of Steiner's life.
    • All of his biographers praise his exemplary lecture notes - not only did he carefully write up the lectures that he attended, he also copied entire lecture courses by for example Steiner and Dirichlet from friends and asked the respective professors to fill in any gaps.
    • Most notable however are his friendships with Steiner and Schlafli, two of the great Swiss mathematicians of the 19th century.
    • Sidler met Steiner during his first stay in Berlin.
    • He reports in his memoirs that he could not attend all of Steiner's lectures, but he seems to have had a habit of demanding a great deal of himself, as in March 1855 Steiner wrote to Schlafli about his lectures [',' J H Graf, Georg Joseph Sidler, Mitteilungen der Naturforschenden Gesellschaft in Bern, 1907, 230-256.','2]: .
    • Steiner spent a lot of time with Sidler during his stay in Bern in 1856-1858 and during the subsequent summers.
    • He seems to have hoped that Sidler would help him formulate mathematical ideas, but this never came to fruition as Steiner suffered a stroke in 1862 and died half a year later.
    • Georg Sidler, Schweizerische Padagogische Zeitschrift 18 (2), 1908, 65-79.','1] that both Sidler and his mother looked after Steiner during those last few months.
    • In the 1880s, Sidler donated a tombstone for Steiner's grave that has been rediscovered in the Bernese cemetery by Butzberger and Moser.
    • He was also involved in placing a memorial plaque on Steiner's last residence in Bern.

  3. Heinrich Schröter (1829-1892)
    • At Berlin he was taught by Lejeune Dirichlet and Jakob Steiner.
    • He attended courses by Dirichlet on number theory and on differential equations which influenced Schroter's teaching for the whole of his career but it was Steiner who was a major influence on Schroter's research.
    • Partly this influence was through the courses Steiner delivered, but his greatest influence on Schroter was through personal contacts.
    • His career in Breslau showed how strongly he had been influenced by Steiner.
    • His first paper Uber die Erzeugnisse krummer projektivischer Gebilde Ⓣ (1857) built on work by Steiner in a paper he published in January 1856.
    • After Steiner's death in 1863 he took over the publication of his posthumous manuscripts, particularly those which were related to the application of the theory of conic sections to projective curves.
    • He edited his transcripts of Steiner's lectures on synthetic geometry which he interweaved with other material by Steiner, together with his own improvements, to produce Jacob Steiner's Vorlesungen uber synthetische Geometrie Ⓣ (1867).
    • This work on the theory of second order surfaces and third order space curves continues Steiner's work.
    • He received the Steiner Prize from the Berlin Academy of Science on 6 July 1876 and, on 6 January 1881 he was elected to the Berlin Academy of Science.
    • In [',' K-R Biermann, Kontroversen um den Steiner-Preis und ihre Folgen.

  4. Julius Plücker (1801-1868)
    • Things were not so simple, however, for the chair of mathematics in Berlin had just been filled by Jakob Steiner.
    • Steiner was the leader of the German school of synthetic geometry, while Plucker followed the analytical approach.
    • Wolfgang Eccarius [',' W Eccarius, Der Gegensatz zwischen Julius Plucker und Jakob Steiner im Lichte ihrer Beziehungen zu August Leopold Crelle : Hintergrunde eines wissenschaftlichen Meinungsstreites, Ann.
    • 37 (2) (1980), 189-213.','12] sees the competition between the two men for the chair of mathematics at the Polytechnic, and August Crelle favouring Plucker over Steiner, as the basis to their personal conflict.
    • His work on combinatorics considers Steiner type systems.
    • Hans Ludwig de Vries writes in [',' H L de Vries, Historical notes on Steiner systems, Discrete Math.
    • It is the aim of these notes to amuse the reader with the remark that already in 1835 Julius Plucker published S(2, 3, 9) in his book 'System der analytischen Geometrie, auf neue Betrachtungsweisen gegrundet, und insbesondere eine ausfuhrliche Theorie der Curven dritter Ordnung enthaltend' Ⓣ and defined general Steiner triple systems S(2, 3, m) = STS(m) there in a footnote.

  5. Ludwig Schläfli (1814-1895)
    • In Bern in 1843 Schlafli met Steiner who was impressed with his language skills and also with his mathematical knowledge.
    • Later that year Steiner, Jacobi and Dirichlet travelled to Rome and took Schlafli with them as an interpreter.
    • Steiner recommended the new travel companion to his Berlin friends saying that Schlafli was a provincial mathematician working near Bern, not very practical but that he learned languages like child's play, and that they should take him with them as a translator.
    • After six months in Italy, Schlafli returned to his teaching post in Thun but he continued to correspond with Steiner till 1856.
    • Ⓣ In one of his letters to Steiner he described the main idea:- .
    • He received the Steiner Prize from the Berlin Academy in 1870 for his discovery of the 27 lines and the 36 double six on the general cubic surface.
    • He was led to this discovery when Steiner told him about Cayley's discovery of the 27 straight lines on the cubic surface.

  6. Karl Geiser (1843-1934)
    • There was a famous mathematician in Karl's family for his great uncle was Jakob Steiner; this certainly helped Karl in his career, particularly when he went to the University of Berlin.
    • Although Geiser was helped in his career by his relationship with Jakob Steiner, he repaid the debt by editing Steiner's unpublished lecture notes and treatises.
    • Auf Grund von Universitatsvortragen und mit Benutzung hinterlassener Manuscripte Jacob Steiner's Ⓣ (1867), Construction der Flache zweiten Grades durch neun Punkte: Nach den hinterlassenen Manuscripten Jacob Steiners dargestellt von Herrn C F Geiser in Zurich Ⓣ (1868), and Zur Erinnerung an Jakob Steiner Ⓣ (1874).
    • In a long and florid address [Geiser] praised the Swiss mathematical glories: Jacob, Johann, and Daniel Bernoulli, Leonhard Euler, and Jakob Steiner.

  7. Thomas Kirkman (1806-1895)
    • He solved the problem of 'Steiner triples' in 1846 in On a Problem in Combinatorics, 6 years before Steiner proposed it.
    • It answered a problem which appeared in the Lady's and Gentleman's Diary of 1845 and shows the existence of 'Steiner systems' seven years before Steiner's article which asked whether such systems existed.
    • After Steiner asked his question, a solution was given by M Reiss in 1859.
    • Despite Kirkman's clear priority, we call such systems today 'Steiner systems' and not 'Kirkman systems'.

  8. Robert Anstice (1813-1853)
    • During his time at Wigginton, Anstice became interested in the mathematical work of another rector, Kirkman, who had written on the subject of Steiner triple systems (as they are now called).
    • In one of his papers Kirkman gave an elegant construction of a resolvable Steiner triple system on 15 elements (the famous Kirkman 15 schoolgirls problem), making use of what are now known as a Room square of order 8 and the Fano plane.
    • Anstice achieved a brilliant generalisation to a resolvable Steiner triple system on 2p + 1 elements for all primes p congruent to 1 modulo 6.
    • He gave infinite families of cyclic Steiner triple systems 40 years before Netto (who did so in 1893).
    • Infinite families of cyclic Steiner triple systems and Room squares are constructed [in the papers].

  9. Martin Gardner (1914-2010)
    • (2) I found a minimal network of Steiner trees that join all the corners of a chessboard.
    • The results Gardner mentions here under (2) appear in the paper "Fan Chung, Martin Gardner and Ron Graham, Steiner trees on a checkerboard, Math.
    • It tells us what kind of Steiner minimum tree a checkerboard should have.
    • The Steiner minimum tree is the shortest network interconnecting the given points.
    • The connection pattern of the Steiner minimum tree for a checkerboard is quite complicated.

  10. Ferdinand Joachimsthal (1818-1861)
    • In 1836 he entered the University of Berlin where he was taught by Lejeune Dirichlet and Jakob Steiner.
    • Steiner had been appointed as an extraordinary professor of geometry two years before Joachimsthal began his studies and he had already made a name for himself as a leading expert on projective geometry.
    • At Berlin, his colleagues included many famous mathematicians who all contributed to his development of mathematical ideas, in particular Gotthold Eisenstein, Lejeune Dirichlet, Carl Jacobi, Jakob Steiner and Carl Borchardt.
    • Influenced by the work of Jacobi, Dirichlet and Steiner, Joachimsthal wrote on the theory of surfaces where he made substantial contributions, particularly to the problem of normals to conic sections and second degree surfaces.
    • The motivation for many of his works were problems posed by other mathematicians, for example he answered questions posed by Pierre Bonnet, Philippe de la Hire, Carl Johann Malmsten (1814-1886), Heinrich Schroter, Jakob Steiner, and Jacques Charles-Francois Sturm.

  11. Fritz (Friedrich) Bützberger (1862-1922)
    • He had a particular interest in Jakob Steiner and published a couple of biographical papers on the geometer.
    • More importantly, he organised and edited Steiner's papers from 1823-26 on the request of the Bernese Society for Natural Scientists.
    • As Butzberger remarks in [',' ETH Library Archive: Hs 194: 114/2, 114/2, F Butzberger, Steinersche Kreis- und Kugelreihen und die Erfindung der Inversion, Beilage zum Programm der Kantonsschule Zurich, Teubner, Leipzig, 1914','3], Graf discovered Steiner's handwritten manuscripts covering the period from 1814 - 1826 in the attic of the Town Library in Bern.
    • Butzberger's Work on Steiner .

  12. August Crelle (1780-1855)
    • In fact Abel and Steiner had strongly encouraged Crelle in his founding of the journal and Steiner was also a major contributor to the first volume of Crelle's Journal.
    • In addition to Abel, mathematicians such as Dirichlet, Eisenstein, Grassmann, Hesse, Jacobi, Kummer, Lobachevsky, Mobius, Plucker, von Staudt, Steiner, and Weierstrass all had their early works made famous by publication in Crelle's journal.

  13. Wilhelm Fiedler (1832-1912)
    • Over the next few years he studied around 250 books including mathematical works by Michel Chasles, Gabriel Lame, Jean Claude Barre de Saint-Venant, Jean-Victor Poncelet, Jakob Steiner, Julius Plucker, Karl von Staudt, George Salmon, Arthur Cayley, and James Joseph Sylvester.
    • Fiedler turned to geometry and studied the ideas of Jakob Steiner, Julius Plucker, August Mobius, Karl von Staudt and the French mathematicians Jean-Victor Poncelet, Michel Chasles and Gabriel Lame.
    • The Prussian Academy of Sciences awarded him their Steiner Prize in 1884 for his book Zyklographie and he received an honorary degree from the University of Technology in Vienna in 1907.

  14. Michel Chasles (1793-1880)
    • The principle of duality occurs throughout his work which was carried further by Steiner.
    • Questions of this type go back to Apollonius, but such questions had arisen while Chasles was working on geometry, in particular the Steiner "problem of five conics" was posed in 1848.
    • This problem, namely to determine the number of conics tangent to five given conics, was solved incorrectly by Steiner who gave the answer 7776.

  15. Wilhelm Blaschke (1885-1962)
    • He favoured Steiner's approach to mathematics which was very much based on geometry and the belief that geometry alone stimulates thinking.
    • This work in particular shows how he was developing ideas due to Steiner who had worked on this topic but was subsequently criticised by Dirichlet for not giving existence proofs.
    • Although Weierstrass had supplied the missing proofs using the calculus of variations, this did not satisfy Blaschke who gave proofs in the style of Steiner in Kreis und Kugel Ⓣ.

  16. Lipót Fejér (1880-1959)
    • Encouraged by Maksay, Fejer began submitting his solutions to the problems to Budapest [',' R Hersh and V John-Steiner, A Visit to Hungarian Mathematics, The Mathematical Intelligencer 15 (2) (1993), 13-26.','6]:- .
    • However, after this his situation quickly became totally unbearable [',' R Hersh and V John-Steiner, A Visit to Hungarian Mathematics, The Mathematical Intelligencer 15 (2) (1993), 13-26.','6]:- .
    • He was fully aware that he was loosing the place and would make comments such as "Since I became a complete idiot." Paul Erdős said (see [',' R Hersh and V John-Steiner, A Visit to Hungarian Mathematics, The Mathematical Intelligencer 15 (2) (1993), 13-26.','6]):- .

  17. Johann Heinrich Graf (1852-1918)
    • He published biographies of a several Swiss mathematicians, cartographers and astronomers, including Ludwig Schlafli and Jakob Steiner.
    • Graf also edited Schlafli's correspondence with Steiner, Arthur Cayley and Carl Borchardt.

  18. Rudolf Sturm (1841-1919)
    • In this work he studied third degree surfaces in their projective representations and proved theorems which had been stated, but not proved, by Steiner.
    • He continued to work on surfaces and, in 1864, he shared with Cremona the Steiner prize of the Berlin Academy for his investigations of surfaces.

  19. Otto Hesse (1811-1874)
    • Hesse's work was also influenced by Steiner, particularly work he did on the geometrical interpretation of algebraic transformations.
    • He was also honoured with the award of the Steiner prize of the Berlin Academy of Sciences in 1872.

  20. Carl Borchardt (1817-1880)
    • He was tutored privately by a number of outstanding tutors, the best known of whom were Plucker and Steiner.
    • Dirichlet and Steiner were also in Rome at the same time and it proved a useful time for Borchardt.

  21. Luigi Cremona (1830-1903)
    • It was this work which won him the Steiner Prize for 1866, the prize being awarded jointly to Cremona and Rudolf Sturm.
    • Many of Steiner's proofs on synthetic geometry were revised and improved by Cremona.

  22. Vojtch Jarník (1897-1970)
    • are devoted to general properties of "Steiner trees." It appears that virtually all general properties of Steiner trees are explicitly stated in [the paper].

  23. Thomas Hirst (1830-1892)
    • In particular he attended lectures by Dirichlet and Steiner, being strongly influenced by Steiner to undertake further research on geometry.

  24. Arnold Droz-Farny (1856-1912)
    • The 1901 paper we mentioned above is, for example, one in which he gives a proof of a theorem stated by Steiner without proof.
    • Droz-Farny's proof appears in the paper Notes sur un theoreme de Steiner Ⓣ in Mathesis 21 (1901), 268-271.

  25. Feodor Theilheimer (1909-2000)
    • Gustav, the son of Raphael Low Theilheimer and Therese Bauer, and Rosa, the daughter of Veiss Nathan Waldmann and Regina Steiner, were married on 18 August 1898.

  26. Siegfried Aronhold (1819-1884)
    • When Jacobi was appointed to the University of Berlin in June 1844, Aronhold followed him and he continued his studies of mathematics in Berlin under Lejeune Dirichlet and Jakob Steiner.

  27. Henry Smith (1826-1883)
    • His first two papers were on geometry and, in 1868, he wrote Certain cubic and biquadratic problems which won him the Steiner prize of the Royal Academy of Berlin.

  28. John Steggall (1855-1935)
    • They include models of: a surface of rotation of the tractrix; a surface of rotation of Steiner's Roman surface, an ellipsoid; a helicoid; a hyperbolic paraboloid; a catenoid; a Riemann surface with branch point of order two; a triply-connected Riemann surface; a hyperbolic paraboloid; a torus; and a hyperboloid of revolution with ellipsoid cross-section.

  29. Theodor Reye (1838-1919)
    • Reye, who was a geometer in the tradition of Steiner and von Staudt, produced about a dozen doctorates during this time.

  30. Wilhelm Ahrens (1872-1927)
    • In 1901 and 1902 he published mathematical chess puzzles; for the 100th anniversary of Carl Jacobi's birth in 1904 he wrote a biography; in 1905 he published a paper on Peter Gustav Lejeune Dirichlet; in 1906 he published letters between Carl Jacobi and his brother Moritz Jacobi concerning Carl Jacobi's unsuccessful attempt in 1848 to become a member of the National Assembly; also in 1906 he published a paper on Jacobi and Steiner; in 1908 he published sketches from the life of Weierstrass; he also wrote several papers discussing whether Euler's works should be published in German or Latin; in 1914 he wrote a couple of papers on one of his favourite topics, namely magic squares, and in the following year on the magic square in Albrecht Durer's painting Melancholia.

  31. James McBride (1868-1949)
    • This paper contains (i) a short history of the geometrical theorem proposed in 1840 by Professor Daniel Christian Ludolph Lehmus (1780-1863) of Berlin to Jacob Steiner - "If BJY, CJZ are equal bisectors of the base angles of a triangle ABC, then AB equals AC," (ii) a selection of some half-dozen solutions from the 50 or 60 that have been given, (iii) some discussion of the logical points raised, and (iv) a list of references to the extensive literature of the subject.

  32. Joseph Gergonne (1771-1859)
    • In addition to Gergonne himself (who published around 200 articles), Poncelet, Servois, Bobillier, Steiner, Plucker, Chasles, Brianchon, Dupin, Lame, Galois and many others had papers appear in the Journal.

  33. Herbert Richmond (1863-1948)
    • In 1885 Cayley and Salmon had carried forward the investigations of the earlier German geometers, Hesse, Steiner, Plucker and other; and Salmon had expounded the subject in treatises which for clarity of style are still unrivalled.

  34. Ágoston Scholtz (1844-1916)
    • In Six points lying on a conic section, and the theorem hexagrammum mysticum (1877) and Sechs Punkte eines Kegelschnittes (1878) he proved Pascal's theorem in Steiner's generality, by reducing it to an equation involving certain determinants.

  35. Rafael Laguardia (1906-1980)
    • Markarian and Accinelli, who were imprisoned with Massera for over three years, wrote the following [',' R Hersh and V John-Steiner, Mathematics as Solace, in Loving and Hating Mathematics: Challenging the Myths of Mathematical Life (Princeton University Press, 2010), 89-105.','1]:- .

  36. George-Henri Halphen (1844-1889)
    • Then, in 1882, he won the Steiner Prize from the Berlin Academy of Sciences for his work on algebraic curves.

  37. Guido Castelnuovo (1865-1952)
    • If the sections of an irreducible algebraic surface with a doubly infinite system of planes turn out to be ruler curves, then the above surface is either ruled or the Roman surface of Steiner.

  38. Adolph Göpel (1812-1847)
    • He wrote on Steiner's synthetic geometry and an important work, published after his death, continued the work of Jacobi on elliptic functions.

  39. Karl Weierstrass (1815-1897)
    • However, he did edit the complete works of Steiner and those of Jacobi.

  40. Adolf Weiler (1851-1916)
    • Weiler's research interests lay in Steiner geometry; in particular, he was interested in complexes and congruencies of rays.

  41. Lejeune Dirichlet (1805-1859)
    • Schlafli and Steiner were also with them, Schlafli's main task being to act as their interpreter but he studied mathematics with Dirichlet as his tutor.

  42. Eduard Heine (1821-1881)
    • He also attended geometry lectures by Steiner, and astronomy lectures by J F Encke, the director of the observatory.

  43. Georg Scheffers (1866-1945)
    • The author quotes with approval the dictum of Jacob Steiner to the effect that construction with the tongue is one thing, and construction with the pen quite another.

  44. Paul Finsler (1894-1970)
    • A large number of treatises and also some books have since been written about "Finslerian geometry" inaugurated in Finsler's dissertation, and it has already become clear that this ground-breaking work is worthy in adding to the Swiss geometric tradition that Steiner and Schlafli began.

  45. Bernhard Riemann (1826-1866)
    • Riemann moved from Gottingen to Berlin University in the spring of 1847 to study under Steiner, Jacobi, Dirichlet and Eisenstein.

  46. Gaston Tarry (1843-1913)
    • He invented what is today called the Tarry point of a triangle which is related to the Brocard triangle and lies on the circumcircle opposite the Steiner point.

  47. Moritz Cantor (1829-1920)
    • He did not take the state examination to qualify as a gymnasium teacher, which most students took at this stage, but he went to Berlin where he spent the summer semester of 1852 attending courses by Lejeune Dirichlet and Jakob Steiner.

  48. Leopold Kronecker (1823-1891)
    • Kronecker became a student at Berlin University in 1841 and there he studied under Dirichlet and Steiner.

  49. Oskar Perron (1880-1975)
    • He introduced this as part of the discussion of Steiner's attempted proof of an isoperimetric problem.

  50. Jean-Baptiste Brasseur (1802-1868)
    • He took over some of his father's courses and published the paper Demonstration d'un theoreme de Steiner Ⓣ in 1865 but, sadly, died in the year this paper was published.

  51. Rudolf Wolf (1816-1893)
    • He moved to Vienna in 1836, studying there for two years before going to Berlin in 1838 where he attended lectures by Encke, Dirichlet, Poggendorf, Steiner and Crelle.

  52. Gustav Roch (1839-1866)
    • Schlomilch received his university education at Berlin under Dirichlet and Steiner.

  53. Philipp von Seidel (1821-1896)
    • In the autumn of 1843 Jacobi left Konigsberg on the grounds of ill health and set off for Italy with Borchardt, Dirichlet, Schlafli and Steiner.

  54. Elwin Christoffel (1829-1900)
    • Christoffel studied at the University of Berlin from 1850 where he was taught by Borchardt, Eisenstein, Joachimsthal, Steiner and Dirichlet.

  55. Alfred Clebsch (1833-1872)
    • These techniques enabled him to rederive with relative ease a number of results that had cost geometers like Jacob Steiner and Otto Hesse a great deal more effort.

  56. Gianfrancesco Malfatti (1731-1807)
    • Jacob Bernoulli had solved the Malfatti problem for an isosceles triangle while, after Malfatti, the problem was also solved by an elegant geometric solution by Jacob Steiner in 1826 and Clebsch solved it using elliptic functions.

  57. Constantin Le Paige (1852-1929)
    • Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.

  58. Carl Jacobi (1804-1851)
    • Schlafli and Steiner were also with them, Schlafli being their interpreter.

  59. Willem 'sGravesande (1688-1742)
    • He maintained an interest in mathematics and science, however, and published Essai de perspective Ⓣ at Leiden in 1711 (see [',' K Andersen, Some observations concerning mathematicians’ treatment of perspective constructions in the 17th and 18th centuries, in Mathemata (Steiner, Wiesbaden, 1985), 409-425.','3] for details).

  60. Hermann Grassmann (1809-1877)
    • The vacancy had occurred since the previous teacher, Jacob Steiner, had just been appointed to a mathematics chair at the University of Berlin.

  61. Walter Hayman (1926-)
    • The author investigates a large number of applications to the theory of functions of two methods of symmetrization: the Steiner method, recently treated by Polya and Szegő, and circular symmetrization, introduced by Polya.

  62. Nicolaas de Bruijn (1918-2012)
    • For example he published On Steiner-Schlafli's hypocycloid (1940) which took a geometrical approach to ideas published by van der Woude earlier that year.

  63. John Semple (1904-1985)
    • In spite, however, of treating geometry algebraically, we have tried never to lose sight of the synthetic approach perfected by such geometers as von Staudt, Steiner, and Reye.

  64. Martin Ohm (1792-1872)
    • His colleagues Steiner and Kummer also ridiculed him for not following Alexander von Humboldt's firm belief in the unity of teaching and research.

  65. Francesco Gerbaldi (1858-1934)
    • In 1881 Gerbaldi published La superficie di Steiner studiata sulla sua rappresentazione analitica mediante le forme ternarie quadratiche Ⓣ which contained his work on conic sections, projective geometry and projective planes.

  66. Joachim Jungius (1587-1657)
    • Ein Beitrag zur Geistesgeschichte des siebzehnten Jahrhunderts (Franz Steiner, Wiesbaden, 1968).','4]) writes:- .

  67. Nathan Mendelsohn (1917-2006)
    • Over the past fifteen years or so, he has turned out a steady stream of extraordinarily innovative papers on Steiner systems and generalizations, orthogonal and perpendicular latin squares, all sorts of block designs, and varieties of groupoids and quasigroups.

  68. Karl von Staudt (1798-1867)
    • Together with Poncelet, Gergonne and Steiner, he belongs to the founders of projective and synthetic geometry.

  69. Arthur Cayley (1821-1895)
    • He was a referee of Kirkman's famous paper in the Cambridge and Dublin Mathematical Journal in which he shows the existence of what today are called Steiner systems.

  70. Michael Freedman (1951-)
    • In the nineteenth century there was a movement, of which Steiner was a principal exponent, to keep geometry pure and ward off the depredations of algebra.


History Topics

  1. Cubic surfaces
    • Steiner already knew of Cayley-Salmon theorem about 27 straight lines when he started his own work on cubic surfaces.
    • Many results on cubic surfaces were stated by Steiner without proof and we shall comment later how Cremona and Rudolf Sturm proved many of these ten years after Steiner's paper.
    • It was Steiner who communicated to Schlafli the Cayley-Salmon theorem on 27 lines on a cubic surface.
    • In this memoir he established many of the properties that had only been stated by Steiner.
    • For his memoir Cremona was awarded a share of the Steiner Prize.
    • He shared the Prize with Rudolf Sturm who studied third degree surfaces in their projective representations and also proved theorems stated, but not proved, by Steiner.
    • Karl Geiser's great uncle was Steiner so he set out on his mathematical career already having links to one of the important figures in the development of the theory of cubic surfaces.

  2. Hirst's diary
    • Steiner .
    • Jakob Steiner: .
    • (7 Nov 1852) Steiner, naturally of a testy disposition, which has been increased, too, by bodily illness, feels himself slighted that he has been 33 years extraordinary professor.

  3. Group theory
    • Steiner in 1832 studied notions of synthetic geometry which were to eventually become part of the study of transformation groups.
      Go directly to this paragraph

  4. Set theory

  5. History overview

  6. Forgery 1
    • If this is so then he had not lost the ability to produce mathematics of the highest quality since his solution of the problem to determine the number of conics tangent to five given conics which he found in 1864 was remarkable, particularly as it corrected a previous incorrect solution by the outstanding mathematician Steiner.

  7. References for Bourbaki 2
    • Wissensch., XII (Steiner, Wiesbaden, 1985), 607-611.

  8. References for Bourbaki 1
    • Wissensch., XII (Steiner, Wiesbaden, 1985), 607-611.


Societies etc

  1. Swiss Mathematical Society
    • In 1930 the Society set up a Committee to look after the archive of material left by Steiner and in 1937 the same committee was also given the responsibility for the archive left by Schlafli.
    • sifting through the legacies of the two great Swiss mathematicians Steiner and Schlafli and making their work accessible.

  2. EMS 1980
    • BACK ROW, Dr R J Steiner, Dr Derek Hacon, Prof Elmer Rees, Mr John Taylor, Dr R F Moss, Dr Lin Sulley, Dr M Nair, Dr M J Beetham, Prof M E Muldoon, Dr T J Laffey, Dr Kyle, Mr Milos Ljeskovac, Dr B Thorpe, Dr W G Griffin, Dr J Popoola, Dr J J O'Connor, Miss Brambilla-Paz, Dr Richard Woolfson, Dr W B Stewart, Mr S P Smith, Dr W A Sutherland, Dr Roy Dyckhoff, Dr Grant Walker, Mr N L Biggs, Dr A G Robertson, Mr R M Wood, Mr A A Jagers, Dr R J Cook, Mr Miles Hoare , Dr Woodward, Mr Stephen A Slebarski, Mr J J Gray, Dr Robert Dawlings, Prof E M Patterson, Dr E F Robertson, Dr A D Sands, Dr R J A Lambourne, Dr C J F Upton, Dr Fereidoun Ghahramani, Mr Con O'Leary, Prof E R Love, .

  3. EMS 1984
    • THIRD ROW, Miss M H M Adamson, Mrs R Adamson, Mr Dimitris Dais, Mr G J Trotter, Dr Alev Eralp, Dr Naoki Kawamoto, Mrs S Lorimer, Mrs Jean Haddow, Dr R Tait, Prof Bruce Shawyer, Mrs E Tait, Dr J O'Connor, Miss Camilla Watters, Dr Edmund F Robertson, Dr A D Sands, Dr Elizabeth A McHarg, Dr J C Amson, Dr R J Steiner, Dr Ray A Ryan, Mr A R Fletcher, Prof T J Laffey, Mr R C Ledgard, .

  4. EMS 1992
    • THIRD ROW, J E Goodman, V 1 Paulsen, J Kaminker, N Ray, A C Kim, P G Hjorth, R J Archbold, R J Steiner, J Hubbuck, D J McLaughlin, P B Guest, N Ruckuc, J C Amson, M-G Leu, B Borwein, 0 Marrero, A J Lazar, T S Blyth, .


Honours

  1. Gibbs Lectures.html
    • January 2001; New Orleans, Louisiana; Ronald L Graham; The Steiner problem.


References

  1. References for Jakob Steiner
    • References for Jakob Steiner .
    • http://www.britannica.com/biography/Jakob-Steiner .
    • C F Geiser, Zur Erinnerung an Jacob Steiner (Schaffhausen, 1874).
    • L Kollros, Jakob Steiner (Basel, 1979).
    • M E Stark and R C Archibald, Jacob Steiner's Geometrical Constructions with a Ruler, Given a Fixed Circle with Its Center (Yeshiva University, 1970).
    • J Steiner, Gesammelte Werke (2 volumes) (Prussian Academy of Sciences, 1881-82).
    • E Begehr and H Lenz, Jacob Steiner and synthetic geometry, in Mathematics in Berlin (Birkhauser, Berlin, 1998), 49-54.
    • K-R Biermann, Jacob Steiner, Nova acta Leopoldina 27 (1963), 31-47.
    • N I Danilova, Problems of Cramer and L'Huilier in the works of Jacob Steiner (Russian), in Questions on the history of mathematical natural science (Akad.
    • W Eccarius, Der Gegensatz zwischen Julius Plucker und Jakob Steiner im Lichte ihrer Beziehungen zu August Leopold Crelle, Hintergrunde eines wissenschaftlichen Meinungsstreites, Ann.
    • J-P Ehrmann, Steiner's theorems on the complete quadrilateral, Forum Geom.
    • D Gallarati, A Steiner theorem (Italian), Archimede 43 (1) (1991), 35-41.
    • J-P Sydler, Apercus sur la vie et l'oeuvre de Jakob Steiner, Enseignement Math.

  2. References for Julius Plücker
    • W Eccarius, Der Gegensatz zwischen Julius Plucker und Jakob Steiner im Lichte ihrer Beziehungen zu August Leopold Crelle : Hintergrunde eines wissenschaftlichen Meinungsstreites, Ann.
    • 48 (Steiner, Stuttgart, 2004), 415-425.
    • H L de Vries, Historical notes on Steiner systems, Discrete Math.

  3. References for Alfréd Rényi
    • R Hersh and V John-Steiner, A Visit to Hungarian Mathematics, The Mathematical Intelligence 15 (2) (1993), 13 - 26.

  4. References for Heinrich Schröter
    • K-R Biermann, Kontroversen um den Steiner-Preis und ihre Folgen.

  5. References for Lipót Fejér
    • R Hersh and V John-Steiner, A Visit to Hungarian Mathematics, The Mathematical Intelligencer 15 (2) (1993), 13-26.

  6. References for Michael Stifel
    • J E Hofmann, Michael Stifel (1487?-1567) : Leben, Wirken und Bedeutung fur die Mathematik seiner Zeit, Sudhoffs Archiv (Franz Steiner Verlag GMBH, Wiesbaden, 1968), 1-42.

  7. References for Willem 'sGravesande
    • K Andersen, Some observations concerning mathematicians' treatment of perspective constructions in the 17th and 18th centuries, in Mathemata (Steiner, Wiesbaden, 1985), 409-425.

  8. References for Nicolas Bourbaki
    • Wissensch., XII (Steiner, Wiesbaden, 1985), 607-611.

  9. References for Gabriel Cramer
    • N I Danilova, Problems of Cramer and L'Huilier in the works of Jacob Steiner (Russian), in Questions on the history of mathematical natural science (Kiev, 1979), 125-135.

  10. References for André Bloch
    • R Hersh and V John-Steiner, Andre Bloch, in Loving and Hating Mathematics: Challenging the Myths of Mathematical Life (Princeton University Press, 2011), 131-133.

  11. References for Bent Christiansen
    • H G Steiner, In Memoriam Bent Christiansen ZDM 29 (1997), 97-101.

  12. References for Karl von Staudt
    • R Fritsch, Karl Georg Christian von Staudt - mathematische und biographische Notizen, in Form, Zahl, Ordnung (Steiner, Stuttgart, 2004), 381-414.

  13. References for Jean-Baptiste-Joseph Delambre
    • Wissensch., XII, Steiner (Wiesbaden, 1985), 493-510.

  14. References for Rafael Laguardia
    • R Hersh and V John-Steiner, Mathematics as Solace, in Loving and Hating Mathematics: Challenging the Myths of Mathematical Life (Princeton University Press, 2010), 89-105.

  15. References for Nicolas-François Canard
    • R Tortajada, Produit net et latitude (Nicolas-Francois Canard, 1754-1833), in Gilbert Facarello et Philippe Steiner (eds), La pensee economique pendant la revolution francaise (Presses Universitaires de Grenoble, Grenoble, 1990), 151-172.

  16. References for Joachim Jungius
    • Ein Beitrag zur Geistesgeschichte des siebzehnten Jahrhunderts (Franz Steiner, Wiesbaden, 1968).

  17. References for Philippe de la Hire
    • D Pingree, Philippe de La Hire's planetary theories in Sanskrit, in From China to Paris: 2000 years transmission of mathematical ideas, Bellagio, 2000 (Steiner, Stuttgart, 2002), 429-453.

  18. References for Karl Weierstrass
    • K-R Biermann, Kontroversen um den Steiner-Preis und ihre Folgen : Ein Kapitel aus den Beziehungen zwischen Weierstrass und Kronecker, Historia Sci.


Additional material

  1. Bützberger on Steiner
    • Butzberger's Work on Steiner .
    • The following account of Butzberger's work on Steiner is taken from the Thesis: C F Geiser and F Rudio: the men behind the First International Congress of Mathematicians by Stefanie Eminger (2014) pp 95-101: http://www-history.mcs.st-and.ac.uk/Publications/Eminger.pdf.
    • Butzberger was an avid Steiner scholar.
    • As one would expect, there are sheets and slips of paper with notes on the topic of his Steiner research, some of them in French or English.
    • There are also a number of manuscripts and drafts of papers relating to Steiner.
    • Among these, a handwritten, 125-page biography of Steiner and a draft of a book on Steiner's mathematical manuscripts 1823-1826 stand out.
    • However, Butzberger did publish two papers on Steiner's life: Jakob Steiner bei Pestalozzi in Yverdon (Jakob Steiner at Pestalozzi's in Yverdon) (1896), and Zum 100.
    • Geburtstage Jakob Steiners (On the Occasion of Jakob Steiner's 100th Birthday) (1896), in which he focuses on Steiner's notebooks as a student at Pestalozzi's school and at university.
    • Indeed, in February 1896 he recommends the paper to the journal's editor Immanuel Carl Volkmar Hoffmann, as Geiser himself 'could not provide [Hoffmann] with the desired article [on Steiner]'.
    • Thank you very much indeed for your exceptionally intriguing paper on Steiner's background.
    • Butzberger must have spent much of his time trying to track down any remaining relatives and friends of Steiner, as well as pictures of and documents relating to him.
    • Among them was his own father-in-law Johann Kohler, who lived about 20 km from Steiner's hometown.
    • Friends of Butzberger, such as Johann Petri, and relatives of Steiner helped as well.
    • Gysel tried to track down a certain Conrad Maurer for him, who seems to have been Steiner's mathematics teacher at Pestalozzi's school.
    • Butzberger showed a particular interest in Steiner's family tree, especially how Steiner and Geiser were related.
    • Another very profitable source of information was Sidler, who inherited some of Steiner's manuscripts and for whom Steiner had been a fatherly friend.
    • Sidler visited [Steiner] almost daily during [Steiner's] bitter time of suffering.
    • In his reply, Sidler suggests changes to the manuscript and gives background information on some points, such as Steiner's character traits and his heirs.
    • Moreover, he recounts some anecdotes that explain Steiner's difficulties with writing and the end of his friendships with Carl Jacobi, Lejeune Dirichlet, and his doctor Johann Schneider.
    • Sidler also comments on the rumour about Steiner's illegitimate daughter.
    • Furthermore, Sidler responds to Butzberger's accusations against Graf and tries to calm him down: According to Butzberger, Graf included some of Butzberger's results regarding Steiner's years in Yverdon in his own papers but failed to reference them.
    • In his Steiner biography, Graf remarks that the Yverdon section is based on Butzberger's paper.
    • The matter of dispute is the year of Steiner's arrival in Yverdon: Butzberger, believing that he settled the issue, cannot understand why Graf revived the debate.
    • In his reply, Graf insists that this must have been a misunderstanding and encloses a postcard with Steiner's birthplace, 'to prove [that he] is not cross with [Butzberger]' -- a rather curious reaction! Whilst Butzberger had a point, his reaction was rather dramatic given the scale of this academic dispute.
    • In fact, both were members of the Steiner-Schlafli Committee, as was Geiser, along with Sidler and five more mathematicians.
    • In a circular of October 1895 the committee explains that its main objective was to raise money for tombs for Steiner and Schlafli.
    • Graf writes that Butzberger and a colleague, Christian Moser, found Steiner's lost grave, and Sidler donated a small tombstone.
    • However, as the graveyard was closed down, the committee successfully applied for permission to exhume Steiner.
    • The committee organised Steiner's re-interment and the erection of a grand tombstone on Schlafli's grave in 1896 to celebrate Steiner's centenary and the anniversary of Schlafli's death (who had died in 1895).
    • Letters from Reye and Emch to Butzberger suggest that he might have planned to publish Steiner's posthumous works.
    • As Hollcroft writes, Butzberger 'died before he had completed the work of editing the Steiner manuscripts'.
    • However, he did publish Uber bizentrische Polygone, Steinersche Kreis- und Kugelreihen und die Erfindung der Inversion (On Bicentric Polygons, Steiner Series of Circles and of Spheres, and the Invention of Inversion) in 1913, dedicating a separate section for each of the three topics.
    • In the second section in particular, he treats 'Steiner series of circles and of spheres; here [he] follows Geiser's view: "Einleitung in die synthetische Geometrie", last chapter "Das Prinzip der reziproken Radien" '.
    • I think that Butzberger's book is very interesting; the first and second sections, in which hardly any new material is included, less so, but certainly the third section, which provides an insight into "Master Steiner's" workshop.
    • Specifically, Butzberger cites a document that he found among Steiner's manuscripts, which proves that Steiner did invent the inversion, as had been suspected previously.
    • Among the papers are excerpts from J Plucker's papers on Steiner's solution of the Malfatti problem (by H Schroter), .
    • https://www-history.mcs.st-andrews.ac.uk/Extras/Butzberger_Steiner.html .

  2. Swart publications
    • O R Oellermann and Henda C Swart, On the Steiner periphery and Steiner eccentricity of a graph, in Topics in combinatorics and graph theory, Oberwolfach, 1990 (Physica, Heidelberg, 1990), 541-547.
    • Michael A Henning, Ortrud R Oellermann and Henda C Swart, On the Steiner radius and Steiner diameter of a graph, Twelfth British Combinatorial Conference (Norwich, 1989), Ars Combin.
    • Michael A Henning, Ortrud R Oellermann and Henda C Swart, On vertices with maximum Steiner [eccentricity in graphs], in Graph theory, combinatorics, algorithms, and applications, San Francisco, CA, 1989 (SIAM, Philadelphia, PA, 1991), 393-403.
    • David P Day, Ortrud R Oellermann and Henda C Swart, Steiner distance-hereditary graphs, SIAM J.
    • Wayne Goddard, Ortrud R Oellermann and Henda C Swart, Steiner distance stable graphs, Discrete Math.
    • Michael A Henning, Ortrud R Oellermann and Henda C Swart, Uniquely Steiner-eccentric graphs, in Graph theory, combinatorics, and algorithms, Vol.
    • Peter Dankelmann, Ortrud R Oellermann and Henda C Swart, The average Steiner distance of a graph, J.
    • Peter Dankelmann, Henda C Swart and Ortrud R Oellermann, On the average Steiner distance of graphs with prescribed properties, 4th Twente Workshop on Graphs and Combinatorial Optimization (Enschede, 1995), Discrete Appl.
    • David P Day, Ortrud R Oellermann and Henda C Swart, A characterization of 3-Steiner distance hereditary graphs, Networks 30 (4) (1997), 243-253.
    • Peter Dankelmann, Henda C Swart and Ortrud R Oellermann, Bounds on the Steiner diameter of a graph, in Combinatorics, graph theory, and algorithms, Vol.

  3. McBride equal bisectors
    • This paper contains (i) a short history of the geometrical theorem proposed in 1840 by Professor Daniel Christian Ludolph Lehmus (1780 - 1863) of Berlin to Jacob Steiner - .
    • Steiner, like most mathematicians, found the theorem "very difficult," and Sylvester remarks, referring to J C Adams - "If report may be believed, intellects capable of extending the bounds of the planetary system, and lighting up new regions of the universe with the torch of analysis, have been baffled by the difficulties of the elementary problem under consideration." (Phil.
    • Steiner gave a fine solution (Crelle's Journal, 1844), both for external and internal bisection, and found an external case where the theorem is not true.
    • (Transversal across two parallel lines makes interior angle-sum on one side equal to two right angles.) We have already rejected, as indirect, proofs of the Contrapositive, like Casey's, Steiner's, etc.

  4. Netto books
    • In the course of further combinatorial operations the author studies systems of triads arising in connection with Kirkmann's and Steiner's problems.
    • Steiner's queries have not yet been fully answered.
    • Skolem's chapter is devoted to groupings of different objects into systems, which may have objects in common; for example, Steiner's arrangement of 7 symbols in threes such that any two occur together in one and only one three.

  5. Tverberg Bergen institute
    • Another paper Uber einige besondere Tripelsysteme mit Anwendung auf die Reproduktion gewisser Quadratsummen bei Multiplikation, in 1931, examined the construction of Steiner triple systems.
    • As interest in the construction of block designs picked up in the 1950s, Skolem realized that there might be interest in some constructions he had previously thought were not new because of their simplicity, and he published two papers On certain distributions of integers in pairs with given differences and Some remarks on the triple systems of Steiner on the subject in 1957 and 1958.
    • This idea has intrinsic appeal, but, as it happens, these partitions and their natural variants can be used in the construction of a host of structures of combinatorial interest, besides the Steiner triple systems for which Skolem originally wanted them.

  6. Who was who 1852
    • Crelle started out with a scoop: five memoirs by the young Norwegian mathematician Niels Henrik Abel (1802-1829) but there were also papers by Carl Gustav Jacob Jacobi (1804-1851) and by Jacob Steiner (1796-1863).
    • At Berlin we also find the brilliant Swiss born geometer Jacob Steiner who, however, never got beyond the extraordinary professorship to which he was appointed in 1834.

  7. Bompiani publications
    • Enrico Bompiani, Sopra certi inviluppi di curve piane e sulle asintotiche della superficie di Steiner, Boll.

  8. Catalan retirement
    • Plus tard, Poisson, Cauchy, Dirichlet, Jacobi, Steiner, Poncelet m'ont accueilli avec une grande bienveillance (*).

  9. Catalan retirement
    • Later, Poisson, Cauchy, Dirichlet, Jacobi, Steiner and Poncelet welcomed me with great kindness (**).

  10. Ahrens publications
    • 'Jacobi' und 'Steiner', Math.

  11. Publications of Alessandro Padoa
    • A Padoa, Esposizione elementare del metodo di Steiner per la risoluzione grafica delle equazioni di 2° grado, Bollettino di Matematica, III (1904), 1.

  12. Righini's publications
    • Galileo e la stella nova, in Prismata, Naturwissenschaftsgeschichtliche Studien (Franz Steiner, Wiesbaden, 1977), 329- .

  13. Fejer descriptions
    • She describes Lipot Fejer, both as teacher and research supervisor, in Reuben Hersh and Vera John-Steiner, "A Visit to Hungarian Mathematics", The Mathematical Intelligencer 15 (2) (1993), 13-26.

  14. J Ruska on Heinrich Suter
    • For several semesters he studied under the supervision of Steiner, and later under Hausheer, then later on continued his studies assiduously in private.

  15. Isaac Schoenberg: Mathematical time exposures
    • Schoenberg offers plenty of geometrical and graphical illustration, but his preferred mode of description is algebraic: indeed, in one essay he acknowledges that "Jakob Steiner, who was a great geometer averse to algebraic calculations, would have heartily disliked our proof of his theorem".

  16. Pál Erds's student years
    • (A visit to Hungarian Mathematics, Reuben Herscb, Vera John-Steiner, The Mathematical Intelligencer Vol 15.

  17. Arvesen publications
    • Ole Peder Arvesen, Sur certaines surfaces algebriques, parmi lesquelles la surface de Steiner constitue le cas le plus simple, Norske Vid.

  18. Pedoe's books
    • In the final chapter, Steiner's proof of the isoperimetric property of the circle is amplified by a careful discussion of the precise meaning of perimeter and area.

  19. Percy MacMahon addresses the British Association in 1901
    • Amongst schoolboys of various ages we note Fresnel, Bessel, Cauchy, Chasles, Lame, Mobius, von Staudt and Steiner on the Continent, and Babbage, Peacock, John Herschel, Henry ParrHamilton and George Green in this country.

  20. Riesz descriptions
    • This quote by Ray Lorch comes from the article by Reuben Hersh and Vera John-Steiner, "A Visit to Hungarian Mathematics", The Mathematical Intelligencer 15 (2) (1993), 13-26: .

  21. Artzy books
    • The geometry is linear, in some places bilinear, and the conics serve principally as sets of pointswhich are infinitely far away, hence Pascal, Brianchon and Steiner have nothing to say.

  22. Semple and Kneebone: 'Algebraic Projective Geometry
    • In spite, however, of treating geometry algebraically, we have tried never to lose sight of the synthetic approach perfected by such geometers as von Staudt, Steiner, and Reye.

  23. Ball books
    • There is a paragraph on the same problem as proposed independently by J Steiner in a somewhat more general form.


Quotations

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Famous Curves

  1. Tricuspoid
    • It was also investigated by Steiner in 1856 and is sometimes called Steiner's hypocycloid.


Chronology

  1. Mathematical Chronology
    • Steiner develops synthetic geometry.
    • Steiner publishes Systematische Entwicklungen ..

  2. Chronology for 1820 to 1830
    • Steiner develops synthetic geometry.

  3. Chronology for 1830 to 1840
    • Steiner publishes Systematische Entwicklungen ..


EMS Archive

  1. EMS 1980
    • BACK ROW, Dr R J Steiner, Dr Derek Hacon, Prof Elmer Rees, Mr John Taylor, Dr R F Moss, Dr Lin Sulley, Dr M Nair, Dr M J Beetham, Prof M E Muldoon, Dr T J Laffey, Dr Kyle, Mr Milos Ljeskovac, Dr B Thorpe, Dr W G Griffin, Dr J Popoola, Dr J J O'Connor, Miss Brambilla-Paz, Dr Richard Woolfson, Dr W B Stewart, Mr S P Smith, Dr W A Sutherland, Dr Roy Dyckhoff, Dr Grant Walker, Mr N L Biggs, Dr A G Robertson, Mr R M Wood, Mr A A Jagers, Dr R J Cook, Mr Miles Hoare , Dr Woodward, Mr Stephen A Slebarski, Mr J J Gray, Dr Robert Dawlings, Prof E M Patterson, Dr E F Robertson, Dr A D Sands, Dr R J A Lambourne, Dr C J F Upton, Dr Fereidoun Ghahramani, Mr Con O'Leary, Prof E R Love, .

  2. EMS Treasurers
    • 2009- R J Steiner .

  3. Colloquium photo 1984
    • THIRD ROW, Miss M H M Adamson, Mrs R Adamson, Mr Dimitris Dais, Mr G J Trotter, Dr Alev Eralp, Dr Naoki Kawamoto, Mrs S Lorimer, Mrs Jean Haddow, Dr R Tait, Prof Bruce Shawyer, Mrs E Tait, Dr J O'Connor, Miss Camilla Watters, Dr Edmund F Robertson, Dr A D Sands, Dr Elizabeth A McHarg, Dr J C Amson, Dr R J Steiner, Dr Ray A Ryan, Mr A R Fletcher, Prof T J Laffey, Mr R C Ledgard, .

  4. Colloquium photo 1992
    • THIRD ROW, J E Goodman, V 1 Paulsen, J Kaminker, N Ray, A C Kim, P G Hjorth, R J Archbold, R J Steiner, J Hubbuck, D J McLaughlin, P B Guest, N Ruskuc, J C Amson, M-G Leu, B Borwein, O Marrero, A J Lazar, T S Blyth, .

  5. Colloquium photo 1980
    • BACK ROW, Dr R J Steiner, Dr Derek Hacon, Prof Elmer Rees, Mr John Taylor, Dr R F Moss, Dr Lin Sulley, Dr M Nair, Dr M J Beetham, Prof M E Muldoon, Dr T J Laffey, Dr Kyle, Mr Milos Ljeskovac, Dr B Thorpe, Dr W G Griffin, Dr J Popoola, Dr J J O'Connor, Miss Brambilla-Paz, Dr Richard Woolfson, Dr W B Stewart, Mr S P Smith, Dr W A Sutherland, Dr Roy Dyckhoff, Dr Grant Walker, Mr N L Biggs, Dr A G Robertson, Mr R M Wood, Mr A A Jagers, Dr R J Cook, Mr Miles Hoare , Dr Woodward, Mr Stephen A Slebarski, Mr J J Gray, Dr Robert Dawlings, Prof E M Patterson, Dr E F Robertson, Dr A D Sands, Dr R J A Lambourne, Dr C J F Upton, Dr Fereidoun Ghahramani, Mr Con O'Leary, Prof E R Love, .


BMC Archive

  1. Minutes for 1989
    • Drs Meldrum and Steiner were appointed as EMS representatives, and five new members were elected to the committee (number of years served in brackets): .
    • R J Steiner EMS Topology .

  2. Minutes for 2000
    • R J Steiner (r.steiner@maths.gla.ac.uk), 53rd BMC, Glasgow, 2001 (Secretary) .

  3. Minutes for 2001
    • Chair: Robert Odoni, Secretary: Richard Steiner.
    • Minutes signed by Richard Steiner (undated).

  4. Minutes for 1990
    • Dr G R Burton (Bath, Secretary) Dr A R Camina (East Anglia) Dr A G Chetwynd (Lancaster) Dr G R Everest (East Anglia) Dr D L Johnson (Nottingham) Prof E C Lance (Leeds, LMS nominee) Dr R R Laxton (Nottingham) Dr P E Newstead (Liverpool) Dr D K Oates (Exeter) Dr A R Pears (KCL, LMS nominee) Dr E F Robertson (St Andrews, EMS nominee) Dr G C Smith (Bath, Chairman) Dr E J Scourfield (REWNC) Dr R J Steiner (Glasgow, EMS nominee) Prof D A R Wallace (Strathclyde) Dr D R Woodall (Nottingham) .

  5. Woodall Mar89.html
    • Drs J D P Meldrum and R J Steiner (for Edinburgh Mathematical Society) .

  6. BMC speakers
    • Steiner, R : 1984 .

  7. Minutes for 1989
    • R B T J Allenby, D A Burgess, A R Camina, C M Campbell, G R Everest, D L Johnson, E C Lance, R R Laxton, A McBride, J D P Meldrum, R W K Odoni, D K Oates, A R Pears, R J Steiner, D R Woodall, F J Yeadon.

  8. BMC 2001
    • The enrolment was 190.nnnnThe chairman was R Odoni and the secretary was R J Steiner.

  9. Minutes for 1992
    • Steiner (Glasgow, EMS Nominee), Dr D.S.G.

  10. BMC 1984
    • Steiner, REquivalences between topology and algebra .

  11. Minutes for 1999
    • Dr R J Steiner (Glasgow), Chairman of the 53rd Colloquium .

  12. Minutes for 1990
    • R J Steiner EMS Topology .

  13. Minutes for 1992
    • Dr R J Steiner (Glasgow) EMS Nominee .

  14. BMC speakers
    • Steiner, R : 1984 .

  15. EMS Mar89.html
    • The EMS will be represented at these meetings by Dr J Meldrum and Dr R Steiner.

  16. Minutes for 1991
    • Dr R J Steiner (Glasgow - EMS nominee) .

  17. BMC Morning speakers
    • Steiner, R : 1984 .

  18. Minutes for 1993
    • Steiner (Glasgow), D.S.G.

  19. Minutes for 1993
    • Dr R J Steiner (EMS) Glasgow .


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