"identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis. Fibonacci Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be ""the most talented Western mathematician of the Middle Ages"". The name he is commonly called, ""Fibonacci"" (), was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for (""son of Bonacci"") and he is also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo (""traveller"") Pisano. Fibonacci popularized the Hindu–Arabic"
"Science and inventions of Leonardo da Vinci Leonardo da Vinci (1452–1519) was an Italian polymath, regarded as the epitome of the ""Renaissance Man"", displaying skills in numerous diverse areas of study. Whilst most famous for his paintings such as the ""Mona Lisa"" and the ""Last Supper"", Leonardo is also renowned in the fields of civil engineering, chemistry, geology, geometry, hydrodynamics, mathematics, mechanical engineering, optics, physics, pyrotechnics, and zoology. While the full extent of his scientific studies has only become recognized in the last 150 years, he was, during his lifetime, employed for his engineering and skill of invention. Many of"
"Leonardo da Vinci Leonardo di ser Piero da Vinci (; 15 April 14522 May 1519), more commonly Leonardo da Vinci or simply Leonardo, was an Italian polymath of the Renaissance whose areas of interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography. He has been variously called the father of palaeontology, ichnology, and architecture, and he is widely considered one of the greatest painters of all time. Sometimes credited with the inventions of the parachute, helicopter, and tank, he epitomised the Renaissance humanist ideal. Many historians and scholars regard Leonardo"
"traditionally spelled ""Mona"" (as used by Vasari), is also commonly spelled in modern Italian as ""Monna Lisa"" ("""" being a vulgarity in some Italian dialects) but this is rare in English. Vasari's account of the ""Mona Lisa"" comes from his biography of Leonardo published in 1550, 31 years after the artist's death. It has long been the best-known source of information on the provenance of the work and identity of the sitter. Leonardo's assistant Salaì, at his death in 1524, owned a portrait which in his personal papers was named ""la Gioconda"", a painting bequeathed to him by Leonardo. That"
"completed the ""Liber Abaci"" (""Book of Abacus"" or ""The Book of Calculation"") which popularized Hindu–Arabic numerals in Europe. Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo) by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens. The date of Fibonacci's death is not known, but it has been estimated to be between 1240 and 1250, most likely in Pisa. In"
"Fibonacci numbers approximates the golden ratio asymptotically as increases. Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, later known as Fibonacci. They appear to have first arisen as early as 200 BC in work by Pingala on enumerating possible patterns of poetry formed from syllables of two lengths. In his 1202 book ""Liber Abaci"", Fibonacci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ""Fibonacci Quarterly"". Applications of Fibonacci"
"Cultural references to Leonardo da Vinci Leonardo da Vinci (April 15, 1452 – May 2, 1519) was an Italian Renaissance painter and polymath who achieved legendary fame and iconic status within his own lifetime. His renown primarily rests upon his brilliant achievements as a painter, the ""Mona Lisa"" and the ""Last Supper"", being two of the most famous artworks ever created, but also upon his diverse skills as a scientist and inventor. He became so highly valued during his lifetime that the King of France bore him home like a trophy of war, supported him in his old age and,"
"every article that appeared in the journal. He also prepared and published the first modern edition of Fibonacci's ""Liber Abaci"". Baldassarre Boncompagni Prince Baldassarre Boncompagni-Ludovisi (10 May 1821 – 13 April 1894), was an Italian historian of mathematics and aristocrat. Boncompagni was born in Rome, into an ancient noble and wealthy Roman family, the Ludovisi-Boncompagni, as the third son of Prince Luigi Boncompagni Ludovisi and Princess Maria Maddalena Odescalchi. He studied under the mathematician Barnabas Dotterel and astronomer Ignazio Calandrelli, developing an interest in the history of science. In 1847 Pope Pius IX appointed him a member of the Accademia"
"his licentiousness, and love of revenge"" (212). Gerolamo Cardano Gerolamo (or Girolamo, or Geronimo) Cardano (; ; ; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler. He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world. He wrote more than 200 works on science. Cardano partially invented and described"
"Poggio Bracciolini Gian Francesco Poggio Bracciolini (11 February 1380 – 30 October 1459), best known simply as Poggio Bracciolini, was an Italian scholar and an early humanist. He was responsible for rediscovering and recovering a great number of classical Latin manuscripts, mostly decaying and forgotten in German, Swiss, and French monastic libraries. His most celebrated find was ""De rerum natura"", the only surviving work by Lucretius. Poggio di Guccio (the surname Bracciolini was added during his career) was born at the village of Terranuova, since 1862 renamed in his honour Terranuova Bracciolini, near Arezzo in Tuscany. Taken by his father"
"remains popular as a printing font today (his friend Niccolò de' Niccoli's script in turn developed into the Italic type, first used by Aldus Manutius in 1501). Poggio Bracciolini Gian Francesco Poggio Bracciolini (11 February 1380 – 30 October 1459), best known simply as Poggio Bracciolini, was an Italian scholar and an early humanist. He was responsible for rediscovering and recovering a great number of classical Latin manuscripts, mostly decaying and forgotten in German, Swiss, and French monastic libraries. His most celebrated find was ""De rerum natura"", the only surviving work by Lucretius. Poggio di Guccio (the surname Bracciolini was"
"Vincenzo Brunacci Vincenzo Brunacci (3 March 1768 – 16 June 1818) was an Italian mathematician born in Florence. He was professor of ""Matematica sublime"" (infinitesimal calculus) in Pavia. He transmitted Lagrange's ideas to his pupils, including Ottaviano Fabrizio Mossotti, Antonio Bordoni and Gabrio Piola. He studied medicine, astronomy and mathematics at the University of Pisa. In 1788 he earned his laurea and the same year he started teaching mathematics at the Navy Institute of Leghorn. In 1796, when Napoleon entered Italy, he endorsed the new order. As a consequence of the Austrian reaction he moved to France between 1799 and"
"Liber Abaci Liber Abaci (also spelled as Liber Abbaci) (""The Book of Calculation"") is a 1202 historic book on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. ""Liber Abaci"" was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols traditionally described as ""Arabic numerals"". By addressing the applications of both commercial tradesmen and mathematicians, it contributed to convincing the public of the superiority of the system, and the use of these glyphs. Although the book's title has also been translated as ""The Book of the Abacus"", writes that this is an error: the"
"some 60 years later. ""Il Puttino, altramente detto il Cavaliere errante"" is a nickname used by Alessandro Salvio for Giovanni Leonardo. According to Alessandro Salvio, Giulio Cesare da Lanciano accompanied Giovanni Leonardo on his way to Madrid until Genoa. After returning to Rome around 1584, Polerio became a chess player and writer in ordinary of Giacomo Boncompagni, Duke of Sora and son of Pope Gregory XIII (born Ugo Boncompagni). Polerio wrote a number of codexes in which a lively international chess is described (exchanges of ideas among Italy, Portugal, and Spain). In these codexes, besides of own and new ideas"
"Pietro Paolo Bonzi Pietro Paolo Bonzi (c. 1576-1636), also known as ""il Gobbo dei Carracci"" (hunchback of the Carracci) or ""il Gobbo dei Frutti"" (of fruits), was an Italian painter, best known for his landscapes and still-lifes. A cartoon of the painter shows his highly deformed lordotic posture. He was born in Cortona, was part of the circle of Annibale Carracci and Domenichino, and trained under Giovanni Battista Viola in Rome. In Rome, he worked for Cardinal Pier Paolo Crescenzi. There are only two still-life paintings known with his signature; he thus was one of the first Italian artists in"
"uncle of Napoleon Bonaparte, who owned another of Leonardo's paintings. Facial features bear only vague resemblance, but landscape, compositional and technical details correspond to those of the ""Mona Lisa"" known worldwide today. A student and companion of Leonardo da Vinci known as Salaì painted one of the nude interpretations of ""Mona Lisa"" known, titled ""Mona Vanna"". Salai's version is thought by some to have been ""based on"" the nude sometimes attributed to Leonardo, which is considered a lost work. Discussion among experts exists as to whether Salai, known to have modeled for Leonardo, may in fact have been the sitter"
"of that kind, and works on chess. His love of elaborate practical jokes is described by Helen Waddell in ""The Wandering Scholars"" (1927). Boncompagno da Signa Boncompagno da Signa (also ""Boncompagnus"" or ""Boncompagni""; c. 1165/1175 – after 1240) was an Italian scholar, grammarian, historian, and philosopher. Born in Signa, near Florence, between 1165 and 1175, he was a professor of rhetoric (""ars dictaminis"") at the University of Bologna and then the University of Padua. In the early thirteenth century, he was one of the first Western European authors to write in the vernacular, in his case Italian. He spent his"
"Gerolamo Cardano Gerolamo (or Girolamo, or Geronimo) Cardano (; ; ; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler. He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world. He wrote more than 200 works on science. Cardano partially invented and described several mechanical devices including the combination lock,"
"Lisa del Giocondo Lisa del Giocondo (; née Gherardini ; June 15, 1479 – July 15, 1542) was an Italian noblewoman, member of the Gherardini family of Florence and Tuscany. Her name was given to the ""Mona Lisa"", her portrait commissioned by her husband and painted by Leonardo da Vinci during the Italian Renaissance. Little is known about Lisa's life. Born in Florence and married in her teens to a cloth and silk merchant who later became a local official, she was a mother to five children and led what is thought to have been a comfortable and ordinary middle-class"
"Michelangelo Buonarroti the Younger Michelangelo Buonarroti il Giovane (baptized 4 November 1568 – 11 January 1646) was a Florentine poet, librettist and man of letters, known as ""the Younger"" to distinguish him from his famous granduncle the sculptor. He studied mathematics at the University of Pisa (1586-1591) where he became friends with Galileo Galilei and Maffeo Barberini, the future Pope Urban VIII. Buonarroti was elected to the Accademia Fiorentina in 1585 and the Accademia della Crusca in 1589, and was one of the editors of first Italian dictionary, ""Vocabolario degli Accademici della Crusca"" (1612). After the wedding of Marie de'"
"Fibonacci numbers, which he used as an example in ""Liber Abaci"". Fibonacci was born around 1175 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia, Algeria). Fibonacci travelled with him as a young boy, and it was in Bugia that he learned about the Hindu–Arabic numeral system. Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which unlike the Roman numerals used at the time, allowed easy calculation using a place-value system. In 1202, he"
"to Nicolaus Venator. Reversing the letters of this construction produces the two star names. They have endured, the result of Cacciatore's little practical joke of naming the two stars after himself. How Webb arrived at this explanation 45 years after the publication of the catalogue is still a mystery. Niccolò Cacciatore Niccolò Cacciatore (; 26 January 1770 – 28 January 1841) was an Italian astronomer. Cacciatore was born at Casteltermini, in Sicily. While studying mathematics and physics in Palermo, he became acquainted with Giuseppe Piazzi, head of the Palermo Astronomical Observatory, and became a graduate student assistant at the observatory"
"posthumously in 1572. Lazarus Buonamici Lazarus (or Lázaro) Buonamici (1479–1552) was an Italian Renaissance humanist. Buonamici was born in Bassano, and studied at the University of Padua. He tutored for the Campeggi family for a time, and later was professor of Belles Lettres at the Sapienza University of Rome. He fled Rome during the sack of 1527, escaping to Padua but losing all his property. He became a professor at Padua, where his lectures acquired for him a great reputation, though he did not commit the results of his scholarship to print, and only a few letters and poems of"
"Giovanni Boccaccio Giovanni Boccaccio (; ; 16 June 1313 – 21 December 1375) was an Italian writer, poet, correspondent of Petrarch, and an important Renaissance humanist. Boccaccio wrote a number of notable works, including ""The Decameron"" and ""On Famous Women"". He wrote his imaginative literature mostly in the Italian vernacular, as well as other works in Latin, and is particularly noted for his realistic dialogue which differed from that of his contemporaries, medieval writers who usually followed formulaic models for character and plot. The details of Boccaccio's birth are uncertain. He was born in Florence or in a village near"
"Domenico Lalli Sebastiano Biancardi (27 March 1679 – 9 October 1741), known by the pseudonym Domenico Lalli, was an Italian poet and librettist. Amongst the many libretti he produced, largely for the opera houses of Venice, were those for Vivaldi's ""Ottone in villa"" and Alessandro Scarlatti's ""Tigrane"". A member of the Accademia degli Arcadi, he also wrote under his arcadian name ""Ortanio"". Lalli was born and raised in Naples as the adopted son of Fulvio Caracciolo but fled the city after being implicated in a bank fraud. After two years wandering about Italy in the company of Emanuele d'Astorga, he"
"Bonaventura Cavalieri Bonaventura Francesco Cavalieri (; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus. Born in Milan, Cavalieri joined the Jesuates order (not to be confused with the Jesuits) at the age of fifteen and remained a member until his death. He studied theology in the monastery of San Gerolamo in Milan, and geometry at the University of Pisa. He"
"Dante Alighieri Durante degli Alighieri (), commonly known by his short name Dante Alighieri or simply as Dante (; , ; – 1321), was a major Italian poet of the Late Middle Ages. His ""Divine Comedy"", originally called ' (modern Italian: ""Commedia"") and later christened ' by Giovanni Boccaccio, is widely considered the most important poem of the Middle Ages and the greatest literary work in the Italian language. In the late Middle Ages, most poetry was written in Latin, accessible only to the most educated readers. In ""De vulgari eloquentia"" (""On Eloquence in the Vernacular""), however, Dante defended the"
"Salaì Gian Giacomo Caprotti da Oreno, better known as Salaì (1480 – before 10 March 1524), was an Italian artist and pupil of Leonardo da Vinci from 1490 to 1518. Salaì entered Leonardo's household at the age of ten. He created paintings under the name of Andrea Salai. He was described as one of Leonardo's students and lifelong servant and is thought by some to be the model for Leonardo's ""St. John the Baptist"" and ""Bacchus"". Salaì was born in 1480 as son of Pietro di Giovanni, a tenant of Leonardo's vineyard near the Porta Vercellina, Milan. He joined Leonardo's"
"Guido Bonatti Guido Bonatti (died between 1296 and 1300) was an Italian mathematician, astronomer and astrologer, who was the most celebrated astrologer of the 13th century. Bonatti was advisor of Frederick II, Holy Roman Emperor, Ezzelino da Romano III, Guido Novello da Polenta and Guido I da Montefeltro. He also served the communal governments of Florence, Siena and Forlì. His employers were all Ghibellines (supporters of the Holy Roman Emperor), who were in conflict with the Guelphs (supporters of the Pope), and all were excommunicated at some time or another. Bonatti's astrological reputation was also criticised in Dante's ""Divine Comedy"","
"Petrarch Francesco Petrarca (; July 20, 1304 – July 18/19, 1374), commonly anglicized as Petrarch (), was a scholar and poet of Renaissance Italy who was one of the earliest humanists. His rediscovery of Cicero's letters is often credited with initiating the 14th-century Renaissance. Petrarch is often considered the founder of Humanism. In the 16th century, Pietro Bembo created the model for the modern Italian language based on Petrarch's works, as well as those of Giovanni Boccaccio, and, to a lesser extent, Dante Alighieri. Petrarch would be later endorsed as a model for Italian style by the Accademia della Crusca."
"one of those who in the 17th and 18th centuries ""redefine[d] the mathematical object"". The lunar crater Cavalerius is named for Cavalieri. Bonaventura Cavalieri Bonaventura Francesco Cavalieri (; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus. Born in Milan, Cavalieri joined the Jesuates order (not to be confused with the Jesuits) at the age of fifteen and remained a member"
"other typefaces and typographical characters. Leonardo da Vinci, born in 1452 in Vinci, was a painter, sculptor, architect, musician, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer. His genius, perhaps more than that of any of his contemporaries, epitomized the creative energy of the Renaissance. He is widely considered to be one of the greatest painters of all time, and his Mona Lisa is regarded by many to be the most famous painting in the world. His anatomical drawings have never been surpassed in detail and accuracy, and are still in use today. Michelangelo was born in Florence in"
"dark? (""quid tum si fuscus Amyntas?"") Violets are black, and hyacinths are black."" Alberti made a variety of contributions to several fields: Leon Battista Alberti Leon Battista Alberti (; February 14, 1404 – April 25, 1472) was an Italian humanist author, artist, architect, poet, priest, linguist, philosopher and cryptographer; he epitomised the Renaissance Man. Although he is often characterized exclusively as an architect, as James Beck has observed, ""to single out one of Leon Battista's 'fields' over others as somehow functionally independent and self-sufficient is of no help at all to any effort to characterize Alberti's extensive explorations in the"