Search Results for Pisa

Biographies

1. Dini biography
   
   • Born: 14 Nov 1845 in Pisa, Italy .
     
   • Died: 28 Oct 1918 in Pisa, Italy .
     
   • It was certainly not a wealthy family but Dini's parents were able to educate him in his native city of Pisa.
     
   • He attended the Scuola Normale Superiore in Pisa which was a teacher's college, under the leadership of Enrico Betti, attached to the University of Pisa.
     
   • Dini returned to Pisa in 1866, and was appointed to a post in the University of Pisa.
     
   • Dini progressed quickly in his career at the University of Pisa, being appointed to Betti's chair of analysis and higher geometry in 1871.
     
   • Despite the workload required in his university career, Dini entered politics in 1871 (although he was only 25 years old at the time) when he was elected to the Pisa City Council.
     
   • In 1877 he was appointed to a second chair in the University of Pisa, from then on holding the chair of infinitesimal analysis in addition to his earlier professorial appointment.
     
   • Having served many times on the Pisa Council, Dini was elected to the national Italian parliament in 1880 as a representative from Pisa.
     
   • Not only was Dini highly involved in teaching mathematics and in local and national politics, but in 1888 he reached the highest office in university administration when he became rector of the University of Pisa.
     

2. Galileo biography
   
   • Born: 15 Feb 1564 in Pisa (now in Italy) .
     
   • Guilia, who was born in Pescia, married Vincenzo in 1563 and they made their home in the countryside near Pisa.
     
   • Galileo was their first child and spent his early years with his family in Pisa.
     
   • However, Galileo remained in Pisa and lived for two years with Muzio Tedaldi who was related to Galileo's mother by marriage.
     
   • When he reached the age of ten, Galileo left Pisa to join his family in Florence and there he was tutored by Jacopo Borghini.
     
   • In 1581 Vincenzo sent Galileo back to Pisa to live again with Muzio Tedaldi and now to enrol for a medical degree at the University of Pisa.
     
   • His mathematics teacher at Pisa was Filippo Fantoni, who held the chair of mathematics.
     
   • In the year 1582-83 Ostilio Ricci, who was the mathematician of the Tuscan Court and a former pupil of Tartaglia, taught a course on Euclid's Elements at the University of Pisa which Galileo attended.
     
   • Of course he was still officially enrolled as a medical student at Pisa but eventually, by 1585, he gave up this course and left without completing his degree.
     
   • Fantoni left the chair of mathematics at the University of Pisa in 1589 and Galileo was appointed to fill the post (although this was only a nominal position to provide financial support for Galileo).
     
   • Galileo spent three years holding this post at the university of Pisa and during this time he wrote De Motu a series of essays on the theory of motion which he never published.
     
   • Being professor of mathematics at Pisa was not well paid, so Galileo looked for a more lucrative post.
     
   • With strong recommendations from Guidobaldo del Monte, Galileo was appointed professor of mathematics at the University of Padua (the university of the Republic of Venice) in 1592 at a salary of three times what he had received at Pisa.
     
   • However he had succeeded in impressing Cosimo and, in June 1610, only a month after his famous little book was published, Galileo resigned his post at Padua and became Chief Mathematician at the University of Pisa (without any teaching duties) and 'Mathematician and Philosopher' to the Grand Duke of Tuscany.
     
   • However he was drawn into the controversy through Castelli who had been appointed to the chair of mathematics in Pisa in 1613.
     

3. Fibonacci biography
   
   • Born: 1170 in (probably) Pisa (now in Italy) .
     
   • Died: 1250 in (possibly) Pisa (now in Italy) .
     
   • His father's job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia.
     
   • Fibonacci ended his travels around the year 1200 and at that time he returned to Pisa.
     
   • Frederick II supported Pisa in its conflicts with Genoa at sea and with Lucca and Florence on land, and he spent the years up to 1227 consolidating his power in Italy.
     
   • Frederick became aware of Fibonacci's work through the scholars at his court who had corresponded with Fibonacci since his return to Pisa around 1200.
     
   • These scholars included Michael Scotus who was the court astrologer, Theodorus Physicus the court philosopher and Dominicus Hispanus who suggested to Frederick that he meet Fibonacci when Frederick's court met in Pisa around 1225.
     
   • This is a decree made by the Republic of Pisa in 1240 in which a salary is awarded to:- .
     

4. Betti biography
   
   • Died: 11 Aug 1892 in Soiana, Pisa, Italy .
     
   • Betti studied mathematics and physics at the University of Pisa and while there he was taught by Mossotti.
     
   • After working as an assistant at the University of Pisa, Betti returned to his home town of Pistoia where he became a teacher of mathematics at a secondary school in the town in 1849.
     
   • He was appointed as professor of higher algebra at the University of Pisa in 1857.
     
   • Back in Pisa he moved in 1859 to the chair of analysis and higher geometry.
     
   • He served a term as rector of the University of Pisa and he became director of its teacher's college, the Scuola Normale Superiore, in 1864 holding this post until his death.
     
   • Under his leadership the Scuola Normale Superiore in Pisa became the leading Italian centre for mathematical research and mathematical education.
     
   • We have already mentioned above that Riemann visited Betti in Pisa in 1863.
     
   • In fact this change of direction by Betti towards mathematical physics led to him substituting chairs at Pisa in 1870 as we remarked above.
     
   • ',4)">4] Bottazzini briefly describes the contents of twelve boxes in the library of the Scuola Normale Superiore in Pisa that contain Betti's unpublished notes and letters.
     

5. Stampacchia biography
   
   • After graduating from the high school, in autumn of 1940 he entered the Science Faculty of the Scuola Normale Superiore of Pisa to study pure mathematics.
     
   • He was given permission to take the university examinations in Pisa in June before being sent to Rome towards the end of month to undergo military training.
     
   • His fourth year of study was therefore at the University of Naples rather than in Pisa.
     
   • He also studied for the Final Examinations of the Scuola Normale Superiore of Pisa which he passed with distinction in November 1945.
     
   • Stampacchia was now offered a position in Pisa but declined the offer and accepted instead a position as an assistant at the Naval Institute at Naples.
     
   • During the period I stayed in Pisa, I tried in several ways to develop a special interest in something, but I wandered among many different topics due to an absolute lack of a guide.
     
   • Thereby, the reasons for the sacrifices I would have to make if I remained in Pisa became all the more meaningless.
     
   • He had been much influenced by Leonida Tonelli, who taught him for a year at Pisa before leaving for Rome, but by this time Tonelli's health was poor; he died in the spring of 1946.
     
   • The years that Stampacchia spent in Pisa and Naples characterize the formation of his personality as an analyst: he was a passionate specialist in calculus of variations and in the theory of partial differential equations, a practitioner and an inspirer of research works of considerable depth and originality of thought.
     
   • When he was invited to return to the Scuola Normale Superiore in Pisa as professor of Higher Analysis in 1970, he gladly accepted.
     
   • In Pisa he undertook a heavy workload.
     
   • One of the main projects Stampacchia had undertaken during his period as professor of Higher Analysis in Pisa was to work on a book on variational inequalities.
     

6. Bertini biography
   
   • Died: 24 Feb 1933 in Pisa, Italy .
     
   • 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 1875 he was appointed professor of geometry at the University of Pisa, accepting the offer of a chair for which he had been proposed by Betti.
     
   • In 1892 Bertini returned to Pisa where he worked until he retired at the age of 75.
     
   • At Pisa, Enriques was his assistant.
     

7. Bianchi biography
   
   • Died: 6 June 1928 in Pisa, Italy .
     
   • Luigi Bianchi was educated at a school in Parma, then at the Scuola Normale Superiore before undertaking university studies at the Pisa.
     
   • He studied under Betti and Dini and graduated with the highest distinction from Pisa in 1877.
     
   • His research was undertaken at a number of universities throughout Europe, first at Pisa, then at Monaco and finally at Gottingen where he studied with Klein.
     
   • After his return to Italy in 1881, Bianchi was appointed to a professorship at the Scuola Normale Superiore of Pisa.
     

8. De Giorgi biography
   
   • Died: 25 Oct 1996 in Pisa, Italy .
     
   • He held this post for less than a year, however, for he was approached by Alexander Faedo who persuaded him to move to the Scuola Normale Superiore at Pisa.
     
   • In the autumn of 1959 De Giorgi moved to Pisa to take up the Chair of Mathematical Analysis [Notices Amer.
     
   • In September 1996 he was taken to hospital in Pisa where he died following an operation.
     

9. Grandi biography
   
   • Died: 4 July 1742 in Pisa, Italy .
     
   • However he continued to teach philosophy being appointed professor in Rome in 1700, then going to Pisa again as professor of philosophy.
     
   • In 1714 Grandi was appointed Professor of Mathematics at the University of Pisa.
     

10. Rosellini biography
    
    • Born: 20 April 1814 in Pisa, Italy .
      
    • Rosellini graduated in mathematics at the University of Pisa and improved his knowledge in physics at the University of Florence, where he was assistant professor to Leopoldo Nobili (1784-1835).
      
    • He perfected his knowledge of French, Latin and Greek, with the help of his brother Ippolito, who by then was professor of Oriental Languages at the University of Pisa.
      

11. Ricci Giovanni biography
    
    • He went to Pisa where he studied mathematics at the Scuola Normale Superiore which is associated with the University of Pisa.
      
    • He returned to Pisa in 1928 when he was appointed as a professor at the Scuola Normale Superiore [Acta Arith.
      
    • As examples of the papers Ricci published during his eight years as a professor in Pisa we mention: Sulle funzioni simmetriche delle radici dell'unita secondo un modulo composto (1931), Sui grandi divisori primi delle coppie di interi in posti corrispondenti di due progressioni aritmetiche.
      
    • Let us also note that, in 1951, Ricci wrote a paper on the school of mathematics in Pisa La scuola matematica pisana dal 1848 al 1948.
      
    • Ricci was unable to continue his research with the vigour that he had in Pisa and was more involved in teaching and administration.
      
    • However his research never returned to the output of his days in Pisa, either in quantity nor depth.
      

12. Enriques biography
    
    • Federigo Enriques's family moved from Livorno to Pisa where Federigo was educated.
      
    • He entered the University of Pisa, also studying at the Scuola Normale in Pisa and he was awarded his degree in 1891.
      
    • He was fortunate to have been taught by Betti in Pisa.
      
    • After his degree, Enriques continued to study at Pisa for a year before moving to Rome to work with Castelnuovo.
      

13. Cavalieri biography
    
    • In 1616 he transferred to the Jesuati monastery in Pisa.
      
    • In Pisa, Cavalieri was taught mathematics by Benedetto Castelli, a lecturer in mathematics at the University of Pisa.
      
    • He also failed to get the chair of mathematics at Pisa when Castelli left for Rome.
      

14. Ricci-Curbastro biography
    
    • He studied there during the years 1872-73, then moved to Pisa where he attended the Scuola Normale Superiore which, under Betti's leadership, was becoming the leading Italian centre for mathematical research and mathematical education.
      
    • As well as attending lectures by Betti in Pisa, Ricci-Curbastro also attended lectures by Dini.
      
    • He remained at Pisa working on a paper which he presented the following year to fulfil the requirements necessary to teach.
      
    • Returning to Pisa in 1879, Ricci-Curbastro became Dini's assistant.
      

15. Libri biography
    
    • His schooling was in Italy where he was well educated before entering the University of Pisa, which he did in 1816.
      
    • sopra la teoria dei numeri in 1820, the year in which he graduated from Pisa.
      
    • Such was the quality of his early work, that he was appointed to the chair of Mathematical Physics at Pisa in 1823.
      

16. Pacioli biography
    
    • He referred also to Leonardo of Pisa (Fibonacci).
      
    • The University of Pisa had suffered a revolt in 1494 and had moved to Florence.
      
    • Pacioli was appointed to teach geometry at the University of Pisa in Florence in 1500.
      

17. Bernstein Felix biography
    
    • Bernstein had, as that stage, no intention of becoming a mathematician and he went to Pisa where he studied philosophy, archaeology and art history.
      
    • Two mathematicians who had heard Cantor heap praise on Bernstein for the Schroder-Bernstein Theorem, persuaded the student of fine arts at Pisa to become a mathematician.
      
    • After his studies at Pisa, he then undertook research under Hilbert and Klein at Gottingen where he wrote the dissertation Untersuchungen aus der Mengenlehre on set theory.
      

18. Pieri biography
    
    • Pieri was awarded a scholarship to study at the Scuola Normale Superiore in Pisa and he began his studies there in November 1881.
      
    • His graduation was on 27 June 1884 and, after graduating, he began teaching at the Technical School in Pisa.
      
    • After teaching only a short while in Pisa, Pieri moved to the Military Academy in Turin where he became professor of projective geometry.
      

19. Volterra biography
    
    • His family were extremely poor (his father had died when Vito was two years old) but after attending lectures at Florence he was able to proceed to Pisa in 1878.
      
    • At Pisa he studied under Betti, graduating Doctor of Physics in 1882.
      
    • He became Professor of Mechanics at Pisa in 1883 and, after Betti's death, he occupied the Chair of Mathematical Physics.
      

20. Dupin biography
    
    • After three years in Corfu he set out to return to France but, while passing through Pisa, he was taken ill.
      
    • It took him a while to recover from the illness, but Dupin was not idle while recovering in Pisa.
      

21. Bombieri biography
    
    • In 1966 Bombieri was appointed to a chair of mathematics at the University of Pisa.
      
    • He began to become interested in problems that De Giorgi and his school of geometric measure theory were working on at the Scuola Normale Superiore in Pisa.
      

22. Beltrami biography
    
    • After two years in Bologna, Beltrami accepted the chair of geodesy at the University of Pisa, which he held from 1864 to 1866.
      
    • At Pisa he became friendly with Betti.
      

23. Fubini biography
    
    • In 1896 Fubini entered the Scuola Normale Superiore di Pisa.
      
    • Fubini remained at Pisa to qualify as a university teacher.
      

24. Fermi biography
    
    • Entry to the Scuola Normale Superiore in Pisa was by competitive examination.
      
    • In Pisa Fermi was advised by the director of the physics laboratory Luigi Puccianti.
      

25. Albanese biography
    
    • Then he entered the Scuola Normale Superiore in Pisa as a student of mathematics and received his doctorate in 1913 having the distinction of receiving the 'Ulisse Dini' prize for his doctoral dissertation Sistemi continui di curve sopra una superficie algebrica (Continuous systems of curves on an algebraic surface).
      
    • Following the award of his doctorate, Albanese was appointed as Dini's assistant at Pisa.
      
    • From 1913 to 1919, as well as his position as assistant, Albanese lectured at the Scuola Normale Superiore in Pisa but he was given leave for military service during the years 1917-18.
      
    • He returned to his position in Pisa at the end of World War I but in 1919 he moved to Padua to become Francesco Severi's assistant.
      
    • From 1929 until 1936 he held the chair of geometry at Pisa, a position which he could have continued to occupy for the rest of his life but he was sent to Brazil in 1936.
      
    • This was in the years in which Albanese became professor of geometry at the University of Catania, going later to Palermo and then to Pisa.
      
    • Albanese spent the rest of his life in São Paulo, holding the chair of Analytical, Projective and Descriptive Geometry, except for the year 1942 when he returned to Pisa because of World War II.
      

26. Ceva Giovanni biography
    
    • Giovanni Ceva was educated in a Jesuit college in Milan, then studied at the university of Pisa.
      
    • He taught at Pisa before being appointed Professor of mathematics at the University of Mantua in 1686, a post he held for the rest of his life.
      

27. Moser Jurgen biography
    
    • Integrable Hamiltonian systems and spectral theory (1983) arises from a course of lectures which Moser gave at the Scuola Normale Superiore in Pisa in 1981.
      
    • Moser was invited to give the Gibbs lecture of the American Mathematical Society in Dallas in 1973, the Pauli lectures at ETH in 1975, the American Mathematical Society Colloquium lectures in Toronto in 1976, the Hardy lectures in Cambridge in 1977, the Fermi lectures in Pisa in 1981, and the John von Neumann Lecture of the Society for Industrial and Applied Mathematics in Seattle in 1984.
      

28. Frisi biography
    
    • He left Milan in 1756 to take up a post as professor of philosophy at the University of Pisa.
      
    • After holding the post in Pisa for eight years, Frisi returned to Milan becoming professor of mathematics at the Scuola Palatina in 1764.
      

29. Gopel biography
    
    • He attended mathematics lectures in Pisa during 1825-26 although he was only 13 years old at the time.
      

30. Alberti biography
    
    • In 1447, the year Nicholas V became Pope, Alberti became a canon of the Metropolitan Church of Florence and Abbot of Sant' Eremita of Pisa.
      

31. Leonardo biography
    
    • By 1503 he was back in Florence advising on the project to divert the River Arno behind Pisa to help with the siege of the city which the Florentines were engaged in.
      

32. Ockham biography
    
    • Ockham had convinced other leading Franciscans of the logic of his arguments, and together they fled to Pisa on 26 May 1328.
      

33. Morera biography
    
    • Morera extended his knowledge of mathematics, first at the University of Pavia in Italy under the direction of Eugenio Beltrami and Felice Casorati, then at the University of Pisa under the direction of Enrico Betti and Ulisse Dini, and finally in Leipzig with Adolph Meyer and Felix Klein.
      

34. Kato biography
    
    • He was invited to give the Fermi Lectures at the Scuola Normale Superiore in Pisa in May 1985.
      

35. Bombelli biography
    
    • The Val di Chiana is a fairly central region in the Tuscan Apennines which was not well drained either by the Arno river which runs north west going through Florence and Pisa to the sea, or by the Tiber which runs south through Rome.
      

36. Blaschke biography
    
    • He spent some time in Pisa with Bianchi, then a semester in Gottingen with Klein, Hilbert and Runge.
      

37. Severi biography
    
    • His final post as assistant was held in Pisa where this time he was assistant to Bertini.
      

38. Danti biography
    
    • Cosimo became first grand duke of Tuscany in 1569 and he appointed Danti to be professor of mathematics at Pisa.
      

39. Eckmann biography
    
    • For example he was a visiting Professor at the University of Michigan during the summer of 1950, the University of Illinois during the winter of 1952, the University of California at Berkeley during the summer of 1955 and the Scuola Normale Superiore in Pisa in the spring of 1958.
      

40. Maior biography
    
    • He became an important avenue through which the writings of the fourteenth-century Mertonians, especially Bradwardine, Heytesbury, and Swineshead, exerted an influence in the schools of the sixteenth century, including those at Padua and Pisa, where the young Galileo received his education.
      

41. Burali-Forti biography
    
    • Cesare Burali-Forti attended the University of Pisa, graduating in 1884.
      

42. Vitali biography
    
    • Giuseppe Vitali graduated from the Scuola Normale Superiore in Pisa in 1899.
      

43. Valerio biography
    
    • On a visit to Pisa in 1590 he met Galileo but it was not until around twenty years later that they entered into a correspondence.
      
    • Their mutual admiration following the publication of Valerio's book led to a renewal of their friendship begun in Pisa fourteen years earlier.
      

44. Gallarati biography
    
    • Dionisio Gallarati entered the University of Pisa in 1941.
      

45. Ruffini biography
    
    • Some mathematicians accepted Ruffini's proof although one would have to say that Pietro Paoli, the professor at Pisa, was influenced by patriotic motives when he wrote in 1799 [Archive for History of Exact Science 23 (1980), 253-277.',4)">4]:- .
      

46. Pincherle biography
    
    • Leaving Marseilles when his schooling was complete, Pincherle entered the University of Pisa in 1869 to study mathematics.
      

47. Castillon biography
    
    • His mother's family was also a noble one originating in Pisa.
      
    • His education was given at home up to the time he entered the University of Pisa.
      
    • There he studied law and mathematics obtaining a doctorate in jurisprudence from Pisa in 1729.
      

48. Fincke biography
    
    • He then attended seven universities over the next five years; Jena, Wittenberg, Heidelberg, Leipzig, Basel, Padua and Pisa.
      

49. Brioschi biography
    
    • In 1858, together with Betti from Pisa and his own student Casorati, Brioschi visited Gottingen, Berlin and Paris.
      

50. Cartan biography
    
    • In the following year he was awarded an honorary doctorate by the University of Pisa.
      

History Topics

1. Mathematics and Architecture references
   
   • K Williams (ed.), Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000).
     
   • F Calio and Marchetti, Generation of architectural forms through linear algebra, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 9-22.
     
   • A Capanna, Conoids and hyperbolic paraboloids in Le Corbusier's Philips Pavilion, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 35-44.
     
   • Y Dold-Samplonius, Calculation of arches and domes in 15th century Samarkand, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 45-55.
     
   • R Fletcher, Golden proportions in a great house : Palladio's Villa Emo, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 73-85.
     
   • L Pepe, Architecture and mathematics in Ferrara from the thirteenth to the eighteenth centuries, Nexus III : architecture and mathematics, Ferrara, 2000 (Pisa, 2000), 87-104.
     
   • M A Reynolds, A new geometric analysis of the Pazzi Chapel in Santa Croce, Florence, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 105-121.
     
   • Z Sagdic, Ottoman architecture: relationships between architectural design and mathematics in architect Sinan's works, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 123-132.
     
   • S R Wassell, Art and mathematics before the Quattrocento : a context for understanding Renaissance architecture, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 157-168.
     

2. Mathematics and Architecture references
   
   • K Williams (ed.), Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000).
     
   • F Calio and Marchetti, Generation of architectural forms through linear algebra, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 9-22.
     
   • A Capanna, Conoids and hyperbolic paraboloids in Le Corbusier's Philips Pavilion, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 35-44.
     
   • Y Dold-Samplonius, Calculation of arches and domes in 15th century Samarkand, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 45-55.
     
   • R Fletcher, Golden proportions in a great house : Palladio's Villa Emo, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 73-85.
     
   • L Pepe, Architecture and mathematics in Ferrara from the thirteenth to the eighteenth centuries, Nexus III : architecture and mathematics, Ferrara, 2000 (Pisa, 2000), 87-104.
     
   • M A Reynolds, A new geometric analysis of the Pazzi Chapel in Santa Croce, Florence, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 105-121.
     
   • Z Sagdic, Ottoman architecture: relationships between architectural design and mathematics in architect Sinan's works, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 123-132.
     
   • S R Wassell, Art and mathematics before the Quattrocento : a context for understanding Renaissance architecture, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 157-168.
     

3. Mathematics and Architecture
   
   • Salingaros writes in [Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 123-132.',27)" onmouseover="window.status='Click to see reference';return true">27]:- .
     
   • The authors of [Nexus III : architecture and mathematics, Ferrara, 2000 (Pisa, 2000), 87-104.',23)" onmouseover="window.status='Click to see reference';return true">23], however, suggest reasons for the occurrence of many of the nice numbers, in particular numbers close to powers of the golden number, as arising from the building techniques used rather than being deliberate decisions of the architects.
     

4. Quadratic etc equations references
   
   • R Franci and T Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus 72 (1985), 17-85.
     

5. Quadratic etc equations references
   
   • R Franci and T Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus 72 (1985), 17-85.
     

6. Classical time
   
   • While attending services in Pisa cathedral be noticed that a swinging lamp in the cathedral took the same time to swing irrespective of how large the displacement.
     

7. Arabic numerals
   
   • Fibonacci writes in his famous book Liber abaci published in Pisa in 1202:- .
     

8. Christianity and Mathematics
   
   • He was drawn into the controversy, however, through Castelli who had been appointed to the chair of mathematics in Pisa in 1613.
     

Famous Curves

1. Rhodonea
   
   • He became professor of philosophy in 1700 and professor of mathematics in 1714 both post being at the University of Pisa.
     

Societies etc

1. Mathematical Circle of Palermo
   
   • In spite of its provincial situation, far from the big intellectual centres of Turin, Pisa and Rome, Guccia had the ambition to make it an international centre for mathematicians of all countries; due to his indefatigable activity and his connections with many foreign mathematicians, he succeeded in bringing the membership of the Circolo to almost one thousand, and in having in his board of editors the most prestigious French and German mathematicians.
     

References

1. References for Fibonacci
   
   • J Gies and F Gies, Leonard of Pisa and the New Mathematics of the Middle Ages (1969).
     
   • I G Basmakova, The 'Liber quadratorum' of Leonardo of Pisa (Russian), in History and methodology of the natural sciences XX (Moscow, 1978), 27-37.
     
   • P K Chong, The life and work of Leonardo of Pisa, Menemui Mat.
     
   • R Franci and L Toti Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus 72 (1-3) (1985), 17-82.
     
   • E Picutti, Leonardo of Pisa's congruous-congruent numbers (Italian), Physis - Riv.
     
   • E Picutti, The 'Book of squares' of Leonardo of Pisa and the problems of indeterminate analysis in the Palatine Codex 557 of the National Library in Florence : Introduction and comments (Italian), Physis - Riv.
     

2. References for Galileo
   
   • M Clavelin, Galilee et la mecanisation du systeme du monde, in Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science I (Dordrecht- Boston, Mass., 1981), 229-251.
     
   • A C Crombie, Philosophical presuppositions and shifting interpretations of Galileo, in Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science I (Dordrecht- Boston, Mass., 1981), 271-286.
     
   • D Gruender, Galileo and the methods of science, in Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science I (Dordrecht- Boston, Mass., 1981), 259-270.
     
   • C B Schmitt, The faculty of arts at Pisa at the time of Galileo, Physis - Riv.
     
   • M Segre, Galileo, Viviani and the tower of Pisa, Stud.
     
   • W L Wisan, Galileo and the emergence of a new scientific style, in Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science I (Dordrecht- Boston, Mass., 1981), 311-339.
     

3. References for Viviani
   
   • A Fabroni, Vitae italorum doctrina excellentium I (Pisa, 1777), 307-344.
     
   • M Segre, Galileo, Viviani and the tower of Pisa, Stud.
     

4. References for Venn
   
   • M Ferriani, L'induzione in John Venn, Quaderni di Storia e Critica della Scienza, Nuova Serie 3, Domus Galilaeana (Pisa, 1973).
     
   • W C Salmon, John Venn's Logic of chance, Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science II (Dordrecht- Boston, Mass., 1981),125-138.
     

5. References for Betti
   
   • U Bottazzini, The mathematical papers of Enrico Betti in the Scuola Normale Superiore of Pisa, Histroia Math.
     

6. References for Grandi
   
   • A Agostini, Padre Guido Grandi matematico, 1671-1742 (Pisa, 1943).
     

7. References for Fermi
   
   • A Gambassi, Enrico Fermi in Pisa, Phys.
     

8. References for De Giorgi
   
   • Pisa Cl.
     

9. References for Bianchi
   
   • Pisa (3) 8 (1954), 43-52.
     

10. References for Pacioli
    
    • R Franci and L Toti Rigatelli, Towards a history of algebra from Leonardo of Pisa to Luca Pacioli, Janus 72 (1-3) (1985), 17-82.
      

11. References for Rosellini
    
    • G Benvenuti, Ferdinando Pio Rosellini patriota ed educatore, Rassegna periodi di informazioni del comune di Pisa 7 (1967), 3-12.
      

Additional material

1. D'Arcy Thompson on Greek irrationals
   
   • This is the famous series, sometimes called the Fibonacci series, supposed to have been 'discovered' or first recorded by Leonardo of Pisa, nicknamed the Son of the Buffalo, or 'Fi Bonacci'.
     

2. Sommerville: 'Geometry of n dimensions
   
   • I am indebted in particular to Schoute's Mehrdimensionale Geometrie (Leipzig, 2 Vols., 1902 and 1905), Bertini's "Introduzione alla geometria proiettiva degli iperspazi" (Pisa, 1907), and the various articles of the "Encyklopadie der mathematischen Wissenschaften." .
     

3. W H and G C Young
   
   • We had otherwise a most pleasant month in Italy, and I particularly remember the last week and the friendly cordiality of Bianchi in Pisa and of Pincherle, Enriquez and Tonelli at Bologna: at this last city, we saw briefly, from a gallery, Einstein giving a lecture , and vainly trying to explain to a protesting audience that the universe is finite but unbounded, finito ma illimitato.
     

Quotations

Chronology