1.
Fibonacci number
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The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, the sequence described in Liber Abaci began with F1 =1. Fibonacci numbers are related to Lucas numbers L n in that they form a complementary pair of Lucas sequences U n = F n and V n = L n. They are intimately connected with the ratio, for example. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is a journal dedicated to their study. The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody, in the Sanskrit tradition of prosody, there was interest in enumerating all patterns of long syllables that are 2 units of duration, and short syllables that are 1 unit of duration. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers, susantha Goonatilake writes that the development of the Fibonacci sequence is attributed in part to Pingala, later being associated with Virahanka, Gopāla, and Hemachandra. He dates Pingala before 450 BC, however, the clearest exposition of the sequence arises in the work of Virahanka, whose own work is lost, but is available in a quotation by Gopala, Variations of two earlier meters. For example, for four, variations of meters of two three being mixed, five happens, in this way, the process should be followed in all mātrā-vṛttas. The sequence is also discussed by Gopala and by the Jain scholar Hemachandra, outside India, the Fibonacci sequence first appears in the book Liber Abaci by Fibonacci. The puzzle that Fibonacci posed was, how many pairs will there be in one year, at the end of the first month, they mate, but there is still only 1 pair. At the end of the month the female produces a new pair. At the end of the month, the original female produces a second pair. At the end of the month, the original female has produced yet another new pair. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs plus the number of pairs alive last month and this is the nth Fibonacci number. The name Fibonacci sequence was first used by the 19th-century number theorist Édouard Lucas, the most common such problem is that of counting the number of compositions of 1s and 2s that sum to a given total n, there are Fn+1 ways to do this. For example, if n =5, then Fn+1 = F6 =8 counts the eight compositions, 1+1+1+1+1 = 1+1+1+2 = 1+1+2+1 = 1+2+1+1 = 2+1+1+1 = 2+2+1 = 2+1+2 = 1+2+2, all of which sum to 5. The Fibonacci numbers can be found in different ways among the set of strings, or equivalently
2.
Otto Fibonacci
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This article contains a list of minor characters in the American television series Prison Break. The listed characters are those who are played by guest stars, the characters are listed alphabetically by their last name or by the name which appears in the episode credits. Jonathan Krantz, or the Pad Man to fans, is the main antagonist in the series and he is the leader of The Company and holds the rank of General. He appears only fleetingly in his first two seasons, as William Kims shadowy superior and architect of Michael Scofields incarceration at Sona. The character plays a large and important role in season 4, in earlier seasons, he is identified by his tendency to issue orders on notepads, to avoid being recorded, a tendency which he fully abandons by the fourth season. In his appearance in the season 4 premiere, he discovers that James Whistler, after Whistlers betrayal, he orders drastic measures to be taken against The Companys enemies, dispatching the ruthless assassin Wyatt to kill anyone and everyone necessary to achieve those ends. When it is reported that Agent Don Self did an identity search on the General, he seems to be very shocked, in Safe and Sound, it is revealed to the viewers that the Generals name is Jonathan Krantz, as seen from the images of him. Learning that the General has one of the Scylla Cards, Michaels team plan an attack against his limo in The Price, due to the betrayal of team member Roland Glenn, the General is alerted and the attack is not successful. Now knowing that Scylla is in danger, the General orders it to be moved and he is tricked in the next episode into thinking that Wyatt has killed the brothers, but decides to go ahead with moving Scylla anyway. He plays a role in Selfless, where he comes face to face with the Scylla team for the first time. When he goes to confront Michael in the bunker, he is forced to hand over his card by Michaels team at gunpoint. Thinking it is useless without the other cards, hes shocked when Michael unlocks Scylla with copies of the five cards. Under duress and the threat of his daughter Lisas life, he allows the Scylla team to escape, in the following episodes, the General is put under immense pressure as he must direct efforts to retrieve Scylla while dealing with dissent amongst his own ranks. After learning in Just Business that Gretchen Morgan and Self has Scylla, he sends his men to retrieve it and his men fail, but capture Michael instead. Discovering that he is in a condition, he is taken back to Company HQ. The General orders the doctors to look after Michael and keep him stable, the General has a somewhat reduced role in these final episodes, often having only a couple of scenes per episode. This is in due to the introduction of a new prominent antagonist. A former employee of The Company, Christina turns rogue and acquires Scylla to set her own plan in motion
3.
Camposanto Monumentale
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The Campo Santo, also known as Camposanto Monumentale or Camposanto Vecchio, is a historical edifice at the northern edge of the Cathedral Square in Pisa, Italy. A legend claims that bodies buried in that ground will rot in just 24 hours, the burial ground lies over the ruins of the old baptistery of the church of Santa Reparata, the church that once stood where the cathedral now stands. The term monumental serves to differentiate it from the urban cemetery in Pisa. The building was the fourth and last one to be raised in the Cathedral Square and it dates from a century after the bringing of the soil from Golgotha, and was erected over the earlier burial ground. The construction of huge, oblong Gothic cloister was begun in 1278 by the architect Giovanni di Simone. He died in 1284 when Pisa suffered a defeat in the battle of Meloria against the Genoans. The cemetery was completed in 1464. It seems that the building was not meant to be a cemetery, but a church called Santissima Trinità. However we know that the part was the western one. The outer wall is composed of 43 blind arches, the one on the right is crowned by a gracious Gothic tabernacle. It contains the Virgin Mary with Child, surrounded by four saints and it is the work from the second half of the 14th century by a follower of Giovanni Pisano. This was the entrance door. Most of the tombs are under the arcades, although a few are on the central lawn, the inner court is surrounded by elaborate round arches with slender mullions and plurilobed tracery. In the Aulla chapel we can see also the original incense lamp that Galileo Galilei used for calculation of pendular movements and this lamp is the one Galileo saw inside the cathedral, now replaced by a larger more elaborate one. The last chapel was Dal Pozzo, commissioned by archbishop of Pisa Carlo Antonio Dal Pozzo in 1594, it has a dedicated to St. Jerome. Also in the Dal Pozzo chapel sometimes a Mass is celebrated, the sarcophagi were initially all around the cathedral, often attached to the building itself. That until the cemetery was built, then they were collected in the all over the meadow. Carlo Lasinio, in the years he was the curator of the Campo Santo, nowadays the sarcophagi are inside the galleries, near the walls
4.
Pisa
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Pisa is a city in Tuscany, Central Italy, straddling the Arno just before it empties into the Tyrrhenian Sea. It is the city of the Province of Pisa. Although Pisa is known worldwide for its tower, the city of over 90,834 residents contains more than 20 other historic churches, several medieval palaces. Much of the architecture was financed from its history as one of the Italian maritime republics. The origin of the name, Pisa, is a mystery, while the origin of the city had remained unknown for centuries, the Pelasgi, the Greeks, the Etruscans, and the Ligurians had variously been proposed as founders of the city. Archaeological remains from the 5th century BC confirmed the existence of a city at the sea, trading with Greeks, the presence of an Etruscan necropolis, discovered during excavations in the Arena Garibaldi in 1991, confirmed its Etruscan origins. Ancient Roman authors referred to Pisa as an old city, strabo referred Pisas origins to the mythical Nestor, king of Pylos, after the fall of Troy. Virgil, in his Aeneid, states that Pisa was already a center by the times described. The Virgilian commentator Servius wrote that the Teuti, or Pelops, the maritime role of Pisa should have been already prominent if the ancient authorities ascribed to it the invention of the naval ram. Pisa took advantage of being the port along the western coast from Genoa to Ostia. Pisa served as a base for Roman naval expeditions against Ligurians, Gauls, in 180 BC, it became a Roman colony under Roman law, as Portus Pisanus. In 89 BC, Portus Pisanus became a municipium, Emperor Augustus fortified the colony into an important port and changed the name in Colonia Iulia obsequens. It is supposed that Pisa was founded on the shore, however, due to the alluvial sediments from the Arno and the Serchio, whose mouth lies about 11 kilometres north of the Arnos, the shore moved west. Strabo states that the city was 4.0 kilometres away from the coast, currently, it is located 9.7 kilometres from the coast. However it was a city, with ships sailing up the Arno. In the 90s AD, a complex was built in the city. During the later years of the Roman Empire, Pisa did not decline as much as the cities of Italy, probably thanks to the complexity of its river system. After Charlemagne had defeated the Lombards under the command of Desiderius in 774, Pisa went through a crisis, politically it became part of the duchy of Lucca
5.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
6.
Liber Abaci
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Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Liber Abaci was among the first Western books to describe Hindu–Arabic numbers 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 Hindu–Arabic numeral system. The title of Liber Abaci means The Book of Calculation, the second version of Liber Abaci was dedicated to Michael Scot in 1227 CE. No versions of the original 1202 CE book have been found, the first section introduces the Hindu–Arabic numeral system, including methods for converting between different representation systems. The second section presents examples from commerce, such as conversions of currency and measurements, another example in this chapter, describing the growth of a population of rabbits, was the origin of the Fibonacci sequence for which the author is most famous today. The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots, the book also includes proofs in Euclidean geometry. Fibonaccis method of solving algebraic equations shows the influence of the early 10th-century Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam, there are three key differences between Fibonaccis notation and modern fraction notation. We generally write a fraction to the right of the number to which it is added. Fibonacci instead would write the same fraction to the left, i. e.132. That is, b a d c = a c + b c d, the notation was read from right to left. For example, 29/30 could be written as 124235 and this can be viewed as a form of mixed radix notation, and was very convenient for dealing with traditional systems of weights, measures, and currency. Sigler also points out an instance where Fibonacci uses composite fractions in which all denominators are 10, Fibonacci sometimes wrote several fractions next to each other, representing a sum of the given fractions. For instance, 1/3+1/4 = 7/12, so a notation like 14132 would represent the number that would now more commonly be written as the mixed number 2712, or simply the improper fraction 3112. Notation of this form can be distinguished from sequences of numerators and denominators sharing a fraction bar by the break in the bar. If all numerators are 1 in a written in this form, and all denominators are different from each other. This notation was also combined with the composite fraction notation. The complexity of this notation allows numbers to be written in different ways. In the Liber Abaci, Fibonacci says the following introducing the Modus Indorum or the method of the Indians, today known as Hindu–Arabic numerals or traditionally, just Arabic numerals
7.
Italians
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Italians are a nation and ethnic group native to Italy who share a common culture, ancestry and speak the Italian language as a native tongue. The majority of Italian nationals are speakers of Standard Italian. Italians have greatly influenced and contributed to the arts and music, science, technology, cuisine, sports, fashion, jurisprudence, banking, Italian people are generally known for their localism and their attention to clothing and family values. The term Italian is at least 3,000 years old and has a history that goes back to pre-Roman Italy. According to one of the common explanations, the term Italia, from Latin, Italia, was borrowed through Greek from the Oscan Víteliú. The bull was a symbol of the southern Italic tribes and was often depicted goring the Roman wolf as a defiant symbol of free Italy during the Social War. Greek historian Dionysius of Halicarnassus states this account together with the legend that Italy was named after Italus, mentioned also by Aristotle and Thucydides. The Etruscan civilization reached its peak about the 7th century BC, but by 509 BC, when the Romans overthrew their Etruscan monarchs, its control in Italy was on the wane. By 350 BC, after a series of wars between Greeks and Etruscans, the Latins, with Rome as their capital, gained the ascendancy by 272 BC, and they managed to unite the entire Italian peninsula. This period of unification was followed by one of conquest in the Mediterranean, in the course of the century-long struggle against Carthage, the Romans conquered Sicily, Sardinia and Corsica. Finally, in 146 BC, at the conclusion of the Third Punic War, with Carthage completely destroyed and its inhabitants enslaved, octavian, the final victor, was accorded the title of Augustus by the Senate and thereby became the first Roman emperor. After two centuries of rule, in the 3rd century AD, Rome was threatened by internal discord and menaced by Germanic and Asian invaders. Emperor Diocletians administrative division of the empire into two parts in 285 provided only temporary relief, it became permanent in 395, in 313, Emperor Constantine accepted Christianity, and churches thereafter rose throughout the empire. However, he moved his capital from Rome to Constantinople. The last Western emperor, Romulus Augustulus, was deposed in 476 by a Germanic foederati general in Italy and his defeat marked the end of the western part of the Roman Empire. During most of the period from the fall of Rome until the Kingdom of Italy was established in 1861, Odoacer ruled well for 13 years after gaining control of Italy in 476. Then he was attacked and defeated by Theodoric, the king of another Germanic tribe, Theodoric and Odoacer ruled jointly until 493, when Theodoric murdered Odoacer. Theodoric continued to rule Italy with an army of Ostrogoths and a government that was mostly Italian, after the death of Theodoric in 526, the kingdom began to grow weak
8.
Republic of Pisa
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The Republic of Pisa was a de facto independent state centered on the Tuscan city of Pisa during the late 10th and 11th centuries. It rose to become a powerhouse, a commercial center whose merchants dominated Mediterranean and Italian trade for a century before being surpassed and superseded by the Republic of Genoa. The power of Pisa as a mighty maritime nation began to grow, during the High Middle Ages the city grew into a very important commercial and naval center and controlled a significant Mediterranean merchant fleet and navy. It expanded its influence through the sack of Reggio di Calabria in the south of Italy in 1005, Pisa was in continuous conflict with the Saracens, whose bases were in the Italian astersa, for control of the Mediterranean. In alliance with Genoa, Sardinia was captured in 1016 with the defeat of the Saracen leader Mujāhid al-‘Āmirī and this victory gave Pisa supremacy in the Tyrrhenian Sea. When the Pisans subsequently ousted the Genoese from Sardinia, a new conflict, between 1030 and 1035 Pisa went on to successfully defeat several rival towns in the Emirate of Sicily and conquer Carthage in North Africa. In 1051-1052 Admiral Jacopo Ciurini conquered Corsica, provoking more resentment from the Genoese. In 1063, the Pisans approached the Norman Roger I of Sicily, Roger declined due to other commitments. With no land support, the Pisan attack against Palermo failed, in 1060 Pisa engaged in its first battle against Genoa and the Pisan victory helped to consolidate its position in the Mediterranean. This was simply a confirmation of the present situation, because at the time the marquis of Tuscany had already excluded from power. Pisa sacked the Zirid city of Mahdia in 1088, four years later, Pisan and Genoese ships helped Alfonso VI of Castile force El Cid out of Valencia. In 1092 Pope Urban II awarded Pisa supremacy over Corsica and Sardinia, a Pisan fleet of 120 ships participated in the First Crusade and the Pisans were instrumental in the siege of Jerusalem in 1099. On their way to the Holy Land the Pisan ships did not miss the opportunity to sack several Byzantine islands, the Pisan crusaders were led by their archbishop, Dagobert, the future Latin Patriarch of Jerusalem. Pisa and the maritime republics took advantage of the crusade to establish trading posts and colonies in the eastern coastal regions of Syria, Lebanon. In particular the Pisans founded colonies in Antioch, Acre, Jaffa, Tripoli, Tyre, in all these cities the Pisans were granted privileges and immunity from taxation, but had to contribute to their defence in case of attack. In the 12th century the Pisan quarter in the part of Constantinople had grown to 1,000 people. For some years of that century Pisa was the most prominent merchant and military ally of the Byzantine Empire, Pisa, as an international power, was destroyed forever by the crushing defeat of its navy in the Battle of Meloria against Genoa in 1284. In this battle, most of the Pisan galleys were destroyed, in 1290, an assault by Genoese ships against the Porto Pisano sealed the fate of the independent Pisan state
9.
Middle Ages
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In the history of Europe, the Middle Ages or Medieval Period lasted from the 5th to the 15th century. It began with the fall of the Western Roman Empire and merged into the Renaissance, the Middle Ages is the middle period of the three traditional divisions of Western history, classical antiquity, the medieval period, and the modern period. The medieval period is subdivided into the Early, High. Population decline, counterurbanisation, invasion, and movement of peoples, the large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the seventh century, North Africa and the Middle East—once part of the Byzantine Empire—came under the rule of the Umayyad Caliphate, although there were substantial changes in society and political structures, the break with classical antiquity was not complete. The still-sizeable Byzantine Empire survived in the east and remained a major power, the empires law code, the Corpus Juris Civilis or Code of Justinian, was rediscovered in Northern Italy in 1070 and became widely admired later in the Middle Ages. In the West, most kingdoms incorporated the few extant Roman institutions, monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks, under the Carolingian dynasty, briefly established the Carolingian Empire during the later 8th, the Crusades, first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims. Kings became the heads of centralised nation states, reducing crime and violence, intellectual life was marked by scholasticism, a philosophy that emphasised joining faith to reason, and by the founding of universities. Controversy, heresy, and the Western Schism within the Catholic Church paralleled the conflict, civil strife. Cultural and technological developments transformed European society, concluding the Late Middle Ages, the Middle Ages is one of the three major periods in the most enduring scheme for analysing European history, classical civilisation, or Antiquity, the Middle Ages, and the Modern Period. Medieval writers divided history into periods such as the Six Ages or the Four Empires, when referring to their own times, they spoke of them as being modern. In the 1330s, the humanist and poet Petrarch referred to pre-Christian times as antiqua, leonardo Bruni was the first historian to use tripartite periodisation in his History of the Florentine People. Bruni and later argued that Italy had recovered since Petrarchs time. The Middle Ages first appears in Latin in 1469 as media tempestas or middle season, in early usage, there were many variants, including medium aevum, or middle age, first recorded in 1604, and media saecula, or middle ages, first recorded in 1625. The alternative term medieval derives from medium aevum, tripartite periodisation became standard after the German 17th-century historian Christoph Cellarius divided history into three periods, Ancient, Medieval, and Modern. The most commonly given starting point for the Middle Ages is 476, for Europe as a whole,1500 is often considered to be the end of the Middle Ages, but there is no universally agreed upon end date. English historians often use the Battle of Bosworth Field in 1485 to mark the end of the period
