Search Results for Cremona

Biographies

1. Cremona biography
   
   • Antonio Luigi Gaudenzio Giuseppe Cremona .
     
   • Luigi Cremona was educated at the Ginnasio in Pavia.
     
   • Political events, however, were to have a major effect on Cremona's life and the first impact came from the revolution of 1848 which attempted to achieve a new and more liberal constitution.
     
   • Cremona, all his life an ardent Italian nationalist, immediately joined the 'Free Italy' battalion.
     
   • Cremona, by this time a sergeant, was with the troops defending Venice.
     
   • Cremona was able to return to Pavia.
     
   • Back in Pavia, Cremona discovered that his mother had died while he had been fighting to free Italy.
     
   • Cremona later wrote, see [Bibliotheca mathematica (1904), 125-195.',6)">6]:- .
     
   • On 9 May 1853 Cremona was awarded his doctorate in civil engineering from the University of Pavia.
     
   • But Austria still controlled the region and this made life hard for Cremona who had fought against the Austrian occupation.
     
   • Cremona was by this time engaged in mathematical research and his first paper appeared in March 1855.
     
   • On 17 January 1857, Cremona was appointed a full teacher at the Ginnasio in Cremona.
     
   • Cremona, the capital of the Cremona region of Lombardy was situated on the north bank of the Po River southeast of Milan.
     
   • Cremona was to remain at the school there for three years and during this time he wrote a number of mathematical articles.
     
   • They are not of great importance except that some of them were examining curves using projective methods, techniques which would be characteristic of Cremona's later important mathematics.
     
   • While the mathematician Cremona taught in the town of Cremona, political events were taking place which would have a large effect on his future.
     
   • Lombardy, liberated from Austrian rule, were quick to see that Cremona should no longer be held back for political reasons.
     
   • With events moving quickly towards a unified Italy under Victor Emmanuel II as King, Cremona was appointed by Royal decree as an ordinary professor at the University of Bologna on 10 June 1860.
     
   • Cremona was to remain in Bologna until October 1867.
     
   • In Cremona's Complete Works there appear 45 articles which he published while at Bologna.
     
   • Also included are Cremona's important work on transformations of plane curves, which were published during this period in 1863 and 1865.
     
   • It was this work which won him the Steiner Prize for 1866, the prize being awarded jointly to Cremona and Rudolf Sturm.
     
   • Also while at Bologna Cremona developed the theory of birational transformations, later known as Cremona transformations, and wrote a series of papers on twisted cubic surfaces.
     
   • White describes this period of Cremona's work in [Bull.
     
   • Chasles was the type on whom at first Cremona modelled his own work.
     
   • Greitzer, writing in [Dictionary of Scientific Biography (New York 1970-1990).',1)">1], describes the importance of Cremona transformations which he introduced in his Bologna period:- .
     
   • Cremona transformations have been used for studying rational surfaces, for the resolution of singularities of plane and space curves, and for the study of elliptic integrals and Riemann surfaces.
     
   • In October 1867, on Brioschi's recommendation, another Royal Decree was issued, this time appointing Cremona to the Polytechnic Institute of Milan.
     
   • The period in Milan, where he remained until 1873, was the time of Cremona's greatest creativity.
     
   • Cremona's work in statics is of great importance and gives, in a clearer form, some theorems due to Maxwell.
     
   • In a paper of 1872 Cremona took an idea of Maxwell's on forces in frame structures that had appeared in an engineering journal in 1867 and interpreted Maxwell's notion of reciprocal figures as duality in projective 3-space.
     
   • In 1873 Cremona was offered a political post as secretary general of the new Italian Government.
     
   • This was a fitting tribute to the highly patriotic Cremona yet his mathematics researches were of such interest that he refused to accept the political post.
     
   • In November 1877, Cremona was appointed to the chair of higher mathematics at the University of Rome.
     
   • On 10 June 1903, after leaving a sickbed to act on some legislation, Cremona succumbed to a heart attack.
     
   • Cremona had a large influence on geometry in Italy.
     
   • Many of Steiner's proofs on synthetic geometry were revised and improved by Cremona.
     
   • Cremona made no startling discoveries in this area: but he did derive many properties of projectively related figures, and he did present the subject to has classes in a manner calculated to clarify and bring out relationships most simply.
     
   • In fact Cremona had a fine reputation as a lecturer [Dictionary of Scientific Biography (New York 1970-1990).',1)">1]:- .
     
   • Cremona was an excellent lecturer: calm, rigorous, yet interesting and even exciting.
     
   • Cremona was extremely fair in citing the works of others, something which was not too common among many mathematicians at that time.
     
   • Cremona himself was conscientious and indefatigable in searching out the work of his predecessors upon matters that he himself was investigating.
     
   • Cremona had many pupils who were to make major contributions to geometry, for example Bertini, Veronese and Guccia.
     
   • Honours awarded to Luigi Cremona .
     
   • Lunar featuresCrater Cremona .
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Cremona.html .
     

2. Gherard biography
   
   • Gherard of Cremona .
     
   • Born: 1114 in Cremona, Italy .
     
   • Gherard of Cremona's name is often written as Gerard or sometimes Gerhard.
     
   • The tremendous upsurge of interest in Arabic and Greek science and philosophy in medieval universities from the start of the thirteenth century owes its stimulation in greater part to the work of Gerard of Cremona.
     

3. Beltrami biography
   
   • Born: 16 Nov 1835 in Cremona, Lombardy, Austrian Empire (now Italy) .
     
   • Influenced by Cremona, Lobachevsky, Gauss and Riemann, Beltrami contributed to work in differential geometry on curves and surfaces.
     
   • The 1868 paper should have appeared sooner but it was delayed in its publication because Cremona was not entirely happy that it was not based on a circular argument.
     
   • Cremona worried that euclidean geometry was being used to describe non-euclidean geometry and he saw a possible logical difficulty in this.
     
   • Cremona was wrong, but his worries caused Beltrami to put his work on one side for a while but the work of Riemann convinced Beltrami that his methods were sound.
     

4. Bertini biography
   
   • While on his engineering studies, Bertini took a mathematics course given by Cremona and this inspired him to study pure mathematics.
     
   • Cremona was an ardent Italian nationalist who, after fighting against the Austrians to help achieve an independent Italy, had been appointed as a professor at Bologna three years before Bertini entered the university.
     
   • Before Bertini could complete his degree he took a break from his studies to take part in the third war for Italian independence, an action which his teacher Cremona strongly approved.
     
   • Bertini returned to his studies at Bologna but was advised by Cremona to transfer to the University of Pisa where he obtained a degree in mathematics in 1867 in the school of Betti and Dini.
     
   • In October 1867 Cremona was appointed to the Polytechnic Institute of Milan.
     
   • Bertini followed his teacher there and, during 1868-69, he studied at Milan attending courses by Cremona, Brioschi and Casorati on Abel's integrals.
     
   • Cremona recommended him to teach descriptive and projective geometry as a lecturer at the University of Rome.
     
   • His work in algebraic geometry extended Cremona's work.
     
   • He studied geometrical properties invariant under Cremona transformations and used the theory to resolve the singularities of a curve.
     

5. Grandi biography
   
   • Born: 1 Oct 1671 in Cremona, Italy .
     
   • Guido Grandi was educated first at the Jesuit college in Cremona.
     

6. Coble biography
   
   • His interests in research relate to finite geometries and the group theory related to them, and to Cremona transformations related to the Galois theory of equations.
     
   • His early papers, written while he was at Johns Hopkins University, include: On the relation between the three-parameter groups of a cubic space curve and a quadric surface (1906); An application of the form-problems associated with certain Cremona groups to the solution of equations of higher degree (1908); An application of Moore's cross-ratio group to the solution of the sextic equation (1911); An application of finite geometry to the characteristic theory of the odd and even theta functions (1913); and Point sets and allied Cremona groups (1915).
     
   • This paper reviews the invariant theory of Cremona transformations as developed by Coble in his earlier papers.
     
   • A linear homogeneous transformation, with integral coefficients, is associated with a Cremona transformations and these transformations form a group which Coble studied.
     

7. Castelnuovo biography
   
   • Rome should be the best place, but unfortunately Cremona is too busy in politics, I don't know how successfully, and he has not been interested in science for a long time.
     
   • In Rome Castelnuovo was a colleague of Cremona but although he had given up active research he was still teaching the Higher Geometry course despite the fact that he had "not been interested in science for a long time", as Veronese had commented five years earlier.
     
   • After Cremona's death in 1903, Castelnuovo began to teach the advanced geometry courses.
     
   • Castelnuovo had only recently graduated when he was informed by Cremona of Kronecker's lecture and he found his own proof of the result.
     

8. Semple biography
   
   • After holding this post for one year (1929-30) he was awarded his doctorate by Cambridge for a thesis on Cremona transformations, was elected a Fellow of St John's College, Cambridge, and, still in the same year 1930, was appointed to the Chair of Pure Mathematics at Queen's University, Belfast.
     
   • chapter VII (Special rational surfaces and plane Cremona transformations) ..
     
   • and also chapter VIII (Linear systems of surfaces, rational manifolds, and higher Cremona transformations), have a rich geometric content and a generous supply of special but highly interesting examples.
     
   • Semple's work was on various aspects of geometry, in particular work on Cremona transformations and work extending results of Severi.
     

9. Castigliano biography
   
   • Cremona chaired a special meeting of the Accademia dei Lincei which was asked to judge whether Menabrea had indeed acted unfairly towards Castigliano.
     
   • Cremona did not find in favour of Castigliano, stating the decision of the committee:- .
     
   • Although Cremona may well have been right in saying that the credit for the principle should go to Menabrea, his claims that Menabrea has the merit of making them popular is less certain.
     
   • To assess the importance of his contribution, however, it is important to note that, although there is some validity in Cremona's attribution of the popularisation of energy methods to Menabrea, it is precisely in this respect that Castigliano excels.
     

10. Noether Max biography
    
    • He was influenced by Abel, Riemann, Cayley and Cremona.
      
    • Following Cremona, Max Noether studied the invariant properties of an algebraic variety under the action of birational transformations.
      
    • For example, he wrote obituaries of Otto Hesse (1875), Arthur Cayley (1895), James Joseph Sylvester (1898), Francesco Brioschi (1898), Sophus Lie (1900), Charles Hermite (1901), Luigi Cremona (1904), George Salmon (1905), Jacob Luroth (1911), Paul Gordan (1914), and Hieronymus Georg Zeuthen (9121).
      

11. Keller biography
    
    • There he submitted his habilitation thesis in 1933 with a work on Cremona transformations.
      
    • In the same year he published two papers related to his thesis, namely Uber eine diskontinuierliche Gruppe von Cremona-Transformationen, and Cremona-Transformationen algebraischer Kurven.
      

12. Hudson biography
    
    • It was a remarkably productive period for Hudson who published her first paper in the Proceedings of the London Mathematical Society in 1911, followed by three papers in 1912, and six papers on topics such as Cremona transformations, nodal curves, pinch-points, and algebraic surfaces in 1913.
      
    • After two years she retired from this position to devote herself to writing the treatise Cremona transformations in plane and space which was published in 1927.
      
    • During the years in which she was writing her major treatise Hudson returned to publishing on Cremona transformations and algebraic surfaces.
      

13. Guccia biography
    
    • Guccia began his studies at the university in Palermo but he later undertook research under Cremona in Rome.
      
    • Guccia himself had four articles appear in the first volume of this publication, the first on Cremona transformations and a generalisation of a theorem due to Hirst, while the second was on a generalisation of a theorem due to Max Noether.
      
    • As we have indicated above, Guccia's work was on geometry, in particular Cremona transformations, classification of curves and projective properties of curves.
      

14. Segre Corrado biography
    
    • The insufficiencies of the earlier theories proposed by A Mobius, Grassmann, Cayley and Cremona were thus soon revealed.
      
    • Segre's contribution to the knowledge of space assures him a place after Cremona in the ranks of the most illustrious members of the new Italian school of geometry.
      

15. Hirst biography
    
    • He became friends with Cremona, particularly sharing his keen involvement in the Italian war of unification.
      
    • His research had been mostly in geometry, in particular on Cremona transformations, and it was for this work that he was awarded the Royal Medal from the Royal Society in 1883.
      

16. Jonquieres biography
    
    • In 1859 de Jonquieres introduced the birational transformation, later studied by Cremona, which is .
      
    • He also studied curve beams, algebraic curves and surfaces, linking his work with that of Salmon, Cayley and Cremona.
      

17. Sturm Rudolf biography
    
    • 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.
      
    • It examines geometric relationships, in particular transformations such as Cremona transformations.
      

18. Veronese biography
    
    • However, he began to correspond with Cremona, who was at the University of Rome, on mathematical topics.
      
    • He started work on a paper on Pascal's hexagram but, following Cremona's advice, he moved to Rome to complete his undergraduate degree.
      

19. Cesaro biography
    
    • Supported by Cremona, Battaglini and Dini, he was awarded a scholarship to allow him to undertake research at the University of Rome which he entered in 1884.
      
    • After one month at the Lycee Terenzio Mamiani, however, Cesaro was offered the chair of mathematics at Palermo and Cremona advised him to accept it.
      

20. Thabit biography
    
    • It was translated into Latin by Gherard of Cremona and became a popular work on mechanics.
      

21. Adelard biography
    
    • Certainly Adelard became an expert in the Arabic language which he might have learnt in Spain as did Gherard of Cremona a few years later.
      

22. Ahmed biography
    
    • Ahmed's work on ratio and proportion was translated into Latin by Gherard of Cremona.
      

23. Banu Musa biography
    
    • This work became well known through the translation into Latin by Gherard of Cremona entitled Liber trium fratum de geometria.
      

24. Weyr biography
    
    • He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach.
      

25. Slaught biography
    
    • His research had been supervised by Eliakim Moore and he was awarded his doctorate for a thesis entitled The Cross Ratio Group of 120 Quadratic Cremona Transformations of the Plane.
      

26. Archimedes biography
    
    • Cremona's translation of On the Sphere and Cylinder (1544) .
      

27. Edge biography
    
    • His work was a continuation of work started by the great geometers of the late 19th and early 20th centuries, in particular Castelnuovo, Cayley, Clebsch, Cremona, Fano, Fricke, Humbert, Klein, Plucker and Schlafli.
      

28. Bianchi biography
    
    • During his time as editor other mathematicians who shared the editorial duties with him include Cremona, Dini, Corrado Segre, Pincherle, Levi-Civita and Severi.
      

29. Brioschi biography
    
    • Casorati was not the only student that Brioschi had in Pavia, for he also advised the doctoral students Cremona (doctorate in 1853) and Beltrami (doctorate in 1856).
      

30. Alexander biography
    
    • Also before 1920 Alexander had made fundamental contributions to the theory of algebraic surfaces and to the study of Cremona transformations.
      

31. Rosanes biography
    
    • In 1870 he provided a demonstration that each plane Cremona transformation can be factored as a product of quadratic transformations, a theorem that Max Noether also proved independently at about the same time.
      

32. Fano biography
    
    • Later work is on algebraic and especially cubic surfaces, as well as on manifolds with a continuous group of Cremona transformations.
      

33. Chisini biography
    
    • As an algebraic geometry researcher, Oscar Chisini is to be considered part of the so-called Italian school, featuring among others Luigi Cremona, Corrado Segre, Guido Castelnuovo, Francesco Severi, Beniamino Segre and, of course, Federigo Enriques.
      

34. Frattini biography
    
    • In 1873 Luigi Cremona arrived in Rome and also taught Frattini who obtained his doctorate in 1875.
      

History Topics

1. Hirst's diary
   
   • Cremona .
     
   • Luigi Cremona: .
     
   • (30 June 1859) [Cremona] is a young man, a pupil of Brioschi's, married and has a family.
     
   • (5 June 1864) [Cremona] had a class of about 12 and lectured on the theory of the sundial in connection with his descriptive geometry.
     

2. 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.
     
   • In March 1866 Cremona published Memoire de geometrie pure sur les surfaces du troisieme ordre.
     
   • For his memoir Cremona was awarded a share of the Steiner Prize.
     

3. Greek sources I
   
   • Gherard of Cremona translated the Thabit version into Latin in the 12th century.
     Go directly to this paragraph
     

4. Tait's scrapbook
   
   • To speak of my own department alone: - what University, home or foreign, has been fortunate enough to see assembled at its celebrations such a collection of the very foremost of the world's mathematicians and physicists as then graced this hall? To name only a very few, we had from the continent Cremona, Helmholtz, Hermite, and Mendeleeff; with Cayley, Salmon, Stokes, Sylvester, and Thomson from our own islands.
     

Famous Curves

Societies etc

1. Cremona
   
   • Luigi Cremona .
     

2. BMC Morning speakers
   
   • Cremona, J : 2008 .
     
   • Cremona, J E : 1995 .
     

3. BMC speakers
   
   • Cremona, J : 2008 .
     
   • Cremona, J E : 1995 .
     

4. Minutes for 2007
   
   • Morning speakers: Anton Cox (City), John Cremona (Warwick), Patrick Dorey (Durham), Ben Green (Cambridge), Dominic Joyce (Oxford), Raphael Rouquier (Oxford), Jonathan Sherratt (Herriot Watt), Caterina Stroppel (Glasgow), Peter Symonds (Manchester), Franco Vivaldi (Queen Mary), Michael Weiss (Aberdeen).
     

5. BMC 1995
   
   • Cremona, J E The arithmetic of elliptic curves .
     

6. BMC 2008
   
   • Cremona, JReduction of binary forms over imaginary quadratic fields.
     

7. Lunar features
   

8. Lunar features
   
   • (W) nnnnn Cremona .
     

9. Lunar features
   
   • Cremona .
     

10. LMS Honorary Member
    
    • 1871 L Cremona .
      

11. Fellows of the RSE
    
    • Luigi Cremona1883More infoMacTutor biography .
      

12. Fellows of the RSE
    
    • Luigi Cremona1883More infoMacTutor biography .
      

13. Fellows of the RSE
    
    • Luigi Cremona1883More infoMacTutor biography .
      

14. Fellow of the Royal Society
    
    • Luigi Cremona 1879 .
      

References

1. References for Cremona
   
   • References for Luigi Cremona .
     
   • Storia di una polemica - una memoria sconosciuta del matematico di Cremona 'Sopra le curve geometriche, o meccaniche', Physis - Riv.
     
   • A Gabba, Le trasformazioni cremoniane in una lettera di Luigi Cremona a Giovanni Schiaparelli, Ist.
     
   • K-R Biermann, Die Wahlvorschlage fur Betti, Brioschi, Beltrami, Casorati und Cremona zu Korrespondierenden Mitgliedern der Berliner Akademie der Wissenschaften, Boll.
     
   • G Loria, Luigi Cremona et son oeuvre mathematique, Bibliotheca mathematica (1904), 125-195.
     
   • Luigi Cremona, Proc.
     
   • Luigi Cremona, Archimede 9 (1957), 137-139.
     
   • M Menghini, Notes on the correspondence between Luigi Cremona and Max Noether, Historia Math.
     
   • H S White, Cremona's works, Bull.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Cremona.html .
     

2. References for Gherard
   
   • H L L Busard, The Latin translation of the Arabic version of Euclid's 'Elements' commonly ascribed to Gerard of Cremona : Introduction, edition and critical apparatus (Leiden, 1984).
     
   • H L L Busard, Einiges uber die Handschrift Leiden 399, 1 und die arabisch-lateinische ubersetzung von Gerhard von Cremona, in History of mathematics (San Diego, CA, 1996), 173-205.
     
   • H L L Busard, Uber einige Euklid-Scholien, die den 'Elementen' von Euklid, ubersetzt von Gerard von Cremona, angehangt worden sind, Centaurus 18 (1973/74), 97-128.
     
   • R Lemay, Gerard of Cremona, Dictionary of the Middle Ages 5 (New York, 1983), 422-423.
     

3. References for Al-Nayrizi
   
   • H L L Busard, Einiges uber die Handschrift Leiden 399, 1 und die arabisch-lateinische ubersetzung von Gerhard von Cremona, in History of mathematics (San Diego, CA, 1996), 173-205.
     

4. References for Casorati
   
   • K-R Biermann, Die Wahlvorschlage fur Betti, Brioschi, Beltrami, Casorati und Cremona zu Korrespondierenden Mitgliedern der Berliner Akademie der Wissenschaften, Boll.
     

5. References for Noether Max
   
   • M Menghini, Notes on the correspondence between Luigi Cremona and Max Noether, Historia Mathematica 13 (4) (1986), 341-351.
     

6. References for Beltrami
   
   • K-R Biermann, Die Wahlvorschlage fur Betti, Brioschi, Beltrami, Casorati und Cremona zu Korrespondierenden Mitgliedern der Berliner Akademie der Wissenschaften, Boll.
     

7. References for Brioschi
   
   • K-R Biermann, Die Wahlvorschlage fur Betti, Brioschi, Beltrami, Casorati und Cremona zu Korrespondierenden Mitgliedern der Berliner Akademie der Wissenschaften, Boll.
     

8. References for Euclid
   
   • H L L Busard, The Latin translation of the Arabic version of Euclid's 'Elements' commonly ascribed to Gerard of Cremona (Leiden, 1984).
     

9. References for Betti
   
   • K-R Biermann, Die Wahlvorschlage fur Betti, Brioschi, Beltrami, Casorati und Cremona zu Korrespondierenden Mitgliedern der Berliner Akademie der Wissenschaften, Boll.
     

Additional material

1. George Chrystal's First Promoter's Address
   
   • On reading the report containing the Italian Bill represented to the Italian Senate by my friend Professor Cremona, I was greatly struck to find that a similar proposal had been made in the original draft of their measure as it came from the former Minister of Education, and that it had been met and overthrown by arguments almost identical with those used by the University of Edinburgh and many others in Scotland.
     
   • Here again the words of the admirable report of Cremona:- "After the qualification has been given, the (free) teaching ought to be given in the buildings of the University, since it does not appear right that the State should have to grant a legal value to courses given beyond all discipline and vigilance.
     

2. Tait's 1888 address to the graduates
   
   • To speak of my own department alone:- what University, home or foreign, has ever been fortunate enough to see assembled at its celebrations such a collection of the very foremost of the world's Mathematicians and Physicists as then graced this bill? To name only a very few, we have had from the continent Cremona, von Helmholtz, Hermite, and Mendeleeff; with Cayley, Salmon, Stokes, Sylvester, and Thomson from our own islands; and almost every other department of knowledge was similarly represented by the elite of its promoters.
     

3. Turnbull lectures on Colin Maclaurin, Part 2
   
   • This wealth of beauty is poured out almost incidentally as the young geometer pursues his way opening up a vast new field and foreshadowing many a theorem or a geometrical principle that was to be significant in the still distant future -- the Cremona transformations, the theory of residuation of Sylvester.
     

4. Tait graduates address.html
   
   • To speak of my own department alone:.what university, home or foreign, has ever been fortunate enough to see assembled at its celebrations such a collection of the very foremost of the world's Mathematicians and Physicists as then graced this bill ? To name only a very few, we have had the continent Cremona, v.
     

5. EMS obituary
   
   • He was about to communicate J G Semple's paper, on Cremona Transformations in [4], and H S M Coxeter's, on Polytopes with regular-prismatic vertex figures, to successive volumes of the Philosophical Transactions.
     

6. Adelard: 'Euclid
   
   • As the large number of manuscripts and the numerous quotations in other scientific and philosophical texts show, it was far better known than the three Euclid translations made from the Arabic in the 12th century (Adelard of Bath, version I; Hermann of Carinthia; Gherard of Cremona).
     

7. Publications of Gino Fano
   
   • G Fano, Ueber Gruppen, insbesondere continuierliche Gruppen von Cremona- Transformationen der Ebene und des Raumes, Monatsh.
     

Quotations

Chronology

1. Chronology for 1100 to 1300
   
   • Gherard of Cremona begins translating Arabic works (and Arabic translations of Greek works) into Latin.
     
   • Arabic numerals are introduced into Europe with Gherard of Cremona's translation of Ptolemy's Almagest.
     

2. Mathematical Chronology
   
   • Gherard of Cremona begins translating Arabic works (and Arabic translations of Greek works) into Latin.
     
   • Arabic numerals are introduced into Europe with Gherard of Cremona's translation of Ptolemy's Almagest.