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History Of Grandi's Series
Geometry and infinite zeros Grandi Guido Grandi (1671–1742) reportedly provided a simplistic account of the series in 1703. He noticed that inserting parentheses into produced varying results: either :(1-1) + (1-1) + \cdots = 0 or :1+(-1+1)+(-1+1) +\cdots = 1. Grandi's explanation of this phenomenon became well known for its religious overtones: In fact, the series was not an idle subject for Grandi, and he didn't think it summed to either 0 or 1. Rather, like many mathematicians to follow, he thought the true value of the series was 1⁄2 for a variety of reasons. Grandi's mathematical treatment of occurs in his 1703 book ''Quadratura circula et hyperbolae per infinitas hyperbolas geometrice exhibita''. Broadly interpreting Grandi's work, he derived through geometric reasoning connected with his investigation of the witch of Agnesi. Eighteenth-century mathematicians immediately translated and summarized his argument in analytical terms: for a generating circle with di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guido Grandi
Guido Grandi Dom Guido Grandi, O.S.B. Cam. (1 October 1671 – 4 July 1742) was an Italian monk, priest, philosopher, theologian, mathematician, and engineer. Life Grandi was born on 1 October 1671 in Cremona, Italy and christened Luigi Francesco Lodovico. When he was of age, he was educated at the Jesuit college there. After he completed his studies there in 1687, he entered the novitiate of the Camaldolese monks at Ferrara and took the name of Guido. In 1693 he was sent to the Monastery of St. Gregory the Great, the Camaldolese house in Rome, to complete his studies in philosophy and theology in preparation for Holy Orders. A year later, Grandi was assigned as professor of both fields at the Camaldolese Monastery of St. Mary of the Angels in Florence. It appears that it was during this period of his life that he took an interest in mathematics. He did his research privately, however, as he was appointed professor of philosophy at St. Gregory Monastery in 1700, subseque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Continuity
The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers. A related law of continuity concerning intersection numbers in geometry was promoted by Jean-Victor Poncelet in his "Traité des propriétés projectives des figures". Leibniz's formulation Leibniz expressed the law in the following terms in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Mercator
Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician. He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he lived from 1642 to 1648 in the Netherlands. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). On 3 May 1661 he observed a transit of Mercury with Christiaan Huygens and Thomas Streete from Long Acre, London. On 14 November 1666 he was elected a Fellow of the Royal Society. He designed a marine chronometer for Charles II. In 1682 Jean Colbert invited Mercator to assist in the design and construction of the fountains at the Palace of Versailles, so he relocated there, but a falling out with Colbert followed. Mathematically, he is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant . However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work '' Ars Conjectandi''.Jacob (Jacques) Bernoulli [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernoulli Positiones 3 Opera
Bernoulli can refer to: People * Bernoulli family of 17th and 18th century Swiss mathematicians: **Daniel Bernoulli (1700–1782), developer of Bernoulli's principle ** Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbers are named **Jacob II Bernoulli (1759–1789) ** Johann Bernoulli (1667–1748) **Johann II Bernoulli (1710–1790) ** Johann III Bernoulli (1744–1807), also known as Jean, astronomer **Nicolaus I Bernoulli (1687–1759) **Nicolaus II Bernoulli (1695–1726) * Elisabeth Bernoulli (1873–1935), Swiss temperance campaigner *Hans Benno Bernoulli (1876–1959), Swiss architect *Ludwig Bernoully (1873–1928), German architect Mathematics * Bernoulli differential equation * Bernoulli distribution and Bernoulli random variable * Bernoulli's inequality * Bernoulli's triangle * Bernoulli number * Bernoulli polynomials * Bernoulli process * Bernoulli trial * Lemniscate of Bernoulli Science * 2034 Bernoulli, minor planet * Bernoulli's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christianity
Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label=Hebrew/Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and religious .... It is the Major religious groups, world's largest and most widespread religion with roughly 2.38 billion followers representing one-third of the global population. Its adherents, known as Christians, are estimated to make up a majority of the population in Christianity by country, 157 countries and territories, and believe that Jesus in Christianity, Jesus is the Son of God (Christianity), Son of God, whose coming as the Messiah#Christianity, messiah was Old Testament messianic prophecies quoted in the New Testament, prophesied in the Hebrew Bible (called the Old Testament in Christianity) and chronicled in the New Testamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and Borders of China, borders fourteen countries by land, the List of countries and territories by land borders, most of any country in the world, tied with Russia. Covering an area of approximately , it is the world's third List of countries and dependencies by area, largest country by total land area. The country consists of 22 provinces of China, provinces, five autonomous regions of China, autonomous regions, four direct-administered municipalities of China, municipalities, and two special administrative regions of China, Special Administrative Regions (Hong Kong and Macau). The national capital is Beijing, and the List of cities in China by population, most populous cit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claudio Filippo Grimaldi
Claudio is an Italian and Spanish first name. In Portuguese it is accented Cláudio. In Catalan and Occitan it is Claudi, while in Romanian it is Claudiu. Origin and history Claudius was the name of an eminent Roman gens, the most important members of which were: * Claudius, Emperor Tiberius Claudius Caesar Augustus Germanicus * Appius Claudius Sabinus Regillensis (fl. 486 BC), founder of the family, originally a Sabine known as Attius Clausus. * Appius Claudius Crassus (fl.450BC), public official, decemvir in 451 BC, appointed to codify the laws. * Appius Claudius Caecus (fl.300BC), official orator, best known for the highway named after him, the Appian Way. Consul in 307 & 296. * Claudius Gothicus (210–270), officer in the Roman army and a provincial governor First name: Claudio Claudio became a popular first name due to the spread of Christianity during the Middle Ages. Claudio is also used in Spanish and in Portuguese, accented as Cláudio. Notable people with the name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missionary
A missionary is a member of a Religious denomination, religious group which is sent into an area in order to promote its faith or provide services to people, such as education, literacy, social justice, health care, and economic development.Thomas Hale 'On Being a Missionary' 2003, William Carey Library Pub, . In the Bible translations into Latin, Latin translation of the Bible, Jesus, Jesus Christ says the word when he sends the disciples into areas and commands them to preach the gospel in his name. The term is most commonly used in reference to Christian missions, but it can also be used in reference to any creed or ideology. The word ''mission'' originated in 1598 when Jesuits, the members of the Society of Jesus sent members abroad, derived from the Latin (nominative case, nom. ), meaning 'act of sending' or , meaning 'to send'. By religion Buddhist missions The first Buddhist missionaries were called "Dharma Bhanaks", and some see a missionary charge in the symbolis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jesuit
The Society of Jesus ( la, Societas Iesu; abbreviation: SJ), also known as the Jesuits (; la, Iesuitæ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rome. It was founded in 1540 by Ignatius of Loyola and six companions, with the approval of Pope Paul III. The society is engaged in evangelization and apostolic ministry in 112 nations. Jesuits work in education, research, and cultural pursuits. Jesuits also give retreats, minister in hospitals and parishes, sponsor direct social and humanitarian ministries, and promote Ecumenism, ecumenical dialogue. The Society of Jesus is consecrated under the patron saint, patronage of Madonna della Strada, a title of the Blessed Virgin Mary, and it is led by a Superior General of the Society of Jesus, Superior General. The headquarters of the society, its Curia, General Curia, is in Rome. The historic curia of Ignatius is now part of the attached to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Traité de mécanique céleste, ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian probability, Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplace operator, Laplacian differential operator, widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaus I Bernoulli
Nicolaus Bernoulli (also spelled Nicolas or Nikolas; 21 October 1687, Basel – 29 November 1759, Basel) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. Biography He was the son of Nicolaus Bernoulli, painter and Alderman of Basel. In 1704 he graduated from the University of Basel under Jakob Bernoulli and obtained his PhD five years later (in 1709) with a work on probability theory in law. His thesis was titled ''Dissertatio Inauguralis Mathematico-Juridica de Usu Artis Conjectandi in Jure''. In 1716 he obtained the Galileo-chair at the University of Padua, where he worked on differential equations and geometry. In 1722 he returned to Switzerland and obtained a chair in Logics at the University of Basel. He was elected a Fellow of the Royal Society of London in March, 1714. His most important contributions can be found in his letters, in particular to Pierre Rémond de Montmort. In these letters, he introduced in particular the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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