Nicholas Mercator
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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, ...
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Gerardus Mercator
Gerardus Mercator (; 5 March 1512 – 2 December 1594) was a 16th-century geographer, cosmographer and Cartography, cartographer from the County of Flanders. He is most renowned for creating the Mercator 1569 world map, 1569 world map based on a new Mercator projection, projection which represented sailing courses of constant bearing (rhumb lines) as straight lines—an innovation that is still employed in nautical charts. Mercator was a highly influential pioneer in the history of cartography.Mark Monmonier, Monmonier, Mark: ''Rhumb Lines and Map Wars: A Social History of the Mercator Projection''. (Chicago: University of Chicago Press, 2004)Van der Krogt, Peter (2015), 'Chapter 6: Gerhard Mercator and his Cosmography: How the 'Atlas' became an Atlas,'; in: Gerhard Holzer, et al. (eds.), ''A World of Innovation: Cartography in the Time of Gerhard Mercator''. (Newcastle upon Tyne: Cambridge Scholars Publishing, 2015), pp. 112–130 Along with Gemma Frisius and Abraham Ortelius, ...
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Transit Of Mercury
frameless, upright=0.5 A transit of Mercury across the Sun takes place when the planet Mercury passes directly between the Sun and a superior planet. During a transit, Mercury appears as a tiny black dot moving across the Sun as the planet obscures a small portion of the solar disk. Because of orbital alignments, transits viewed from Earth occur in May or November. The last four such transits occurred on May 7, 2003; November 8, 2006; May 9, 2016; and November 11, 2019. The next will occur on November 13, 2032. A typical transit lasts several hours. Mercury transits are much more frequent than transits of Venus, with about 13 or 14 per century, primarily because Mercury is closer to the Sun and orbits it more rapidly. On June 3, 2014, the Mars rover ''Curiosity'' observed the planet Mercury transiting the Sun, marking the first time a planetary transit has been observed from a celestial body besides Earth. Scientific investigation The orbit of the planet Mercury lies interi ...
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Mathematics Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing ...
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53 Equal Temperament
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency ratios). Each step represents a frequency ratio of 2, or 22.6415  cents (), an interval sometimes called the Holdrian comma. 53-TET is a tuning of equal temperament in which the tempered perfect fifth is 701.89 cents wide, as shown in Figure 1. The 53-TET tuning equates to the unison, or ''tempers out'', the intervals , known as the schisma, and , known as the kleisma. These are both 5 limit intervals, involving only the primes 2, 3 and 5 in their factorization, and the fact that 53 ET tempers out both characterizes it completely as a 5 limit temperament: it is the only regular temperament tempering out both of these intervals, or commas, a fact which seems to have first been recognized by Japanese music theorist Shohé Tanaka. Because it tempers these out, 53-TET can b ...
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Mercator Series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural logarithm (shifted by 1) whenever -1 .


History

The series was discovered independently by Johannes Hudde and . It was first published by , in his 1668 treatise ''Logarithmotechnia''.


Derivation

The series can be obtained from

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Logarithms
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base''  is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number  as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accura ...
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Encyclopedia
An encyclopedia (American English) or encyclopædia (British English) is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles or entries that are arranged alphabetically by article name or by thematic categories, or else are hyperlinked and searchable. Encyclopedia entries are longer and more detailed than those in most dictionaries. Generally speaking, encyclopedia articles focus on '' factual information'' concerning the subject named in the article's title; this is unlike dictionary entries, which focus on linguistic information about words, such as their etymology, meaning, pronunciation, use, and grammatical forms.Béjoint, Henri (2000)''Modern Lexicography'', pp. 30–31. Oxford University Press. Encyclopedias have existed for around 2,000 years and have evolved considerably during that time as regards language (written in a major international or a ...
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Palace Of Versailles
The Palace of Versailles ( ; french: Château de Versailles ) is a former royal residence built by King Louis XIV located in Versailles, about west of Paris, France. The palace is owned by the French Republic and since 1995 has been managed, under the direction of the French Ministry of Culture, by the Public Establishment of the Palace, Museum and National Estate of Versailles. Some 15,000,000 people visit the palace, park, or gardens of Versailles every year, making it one of the most popular tourist attractions in the world. Louis XIII built a simple hunting lodge on the site of the Palace of Versailles in 1623 and replaced it with a small château in 1631–34. Louis XIV expanded the château into a palace in several phases from 1661 to 1715. It was a favorite residence for both kings, and in 1682, Louis XIV moved the seat of his court and government to Versailles, making the palace the ''de facto'' capital of France. This state of affairs was continued by Kings Louis XV a ...
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Jean Colbert
Jean-Baptiste Colbert (; 29 August 1619 – 6 September 1683) was a French statesman who served as First Minister of State from 1661 until his death in 1683 under the rule of King Louis XIV. His lasting impact on the organization of the country's politics and markets, known as Colbertism, a doctrine often characterized as a variant of mercantilism, earned him the nickname ''le Grand Colbert'' (; "the Great Colbert"). A native of Reims, he was appointed Intendant of Finances on 4 May 1661. Colbert took over as Controller-General of Finances, a newly elevated position, in the aftermath of the arrest of Nicolas Fouquet for embezzlement, an event that led to the abolishment of the office of Superintendent of Finances. He worked to develop the domestic economy by raising tariffs and encouraging major public works projects, as well as to ensure that the French East India Company had access to foreign markets, so that they could always obtain coffee, cotton, dyewoods, fur, pepper, ...
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Thomas Birch
Thomas Birch (23 November 17059 January 1766) was an English historian. Life He was the son of Joseph Birch, a coffee-mill maker, and was born at Clerkenwell. He preferred study to business but, as his parents were Quakers, he did not go to the university. Notwithstanding this circumstance, he was ordained deacon in the Church of England in 1730 and priest in 1731. As a strong supporter of the Whigs, he gained the favour of Philip Yorke, afterwards Lord Chancellor and first Earl of Hardwicke, and his subsequent preferments were largely due to this friendship. He held successively a number of benefices in different counties, and finally in London. He was noted as a keen fisherman during the course of his lifetime, and devised an unusual method of disguising his intentions. Dressed as a tree, he stood by the side of a stream in an outfit designed to make his arms seem like branches and the rod and line a spray of blossom. Any movement, he argued, would be taken by a fish to be ...
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Charles II Of England
Charles II (29 May 1630 – 6 February 1685) was King of Scotland from 1649 until 1651, and King of England, Scotland and Ireland from the 1660 Restoration of the monarchy until his death in 1685. Charles II was the eldest surviving child of Charles I of England, Scotland and Ireland and Henrietta Maria of France. After Charles I's execution at Whitehall on 30 January 1649, at the climax of the English Civil War, the Parliament of Scotland proclaimed Charles II king on 5 February 1649. But England entered the period known as the English Interregnum or the English Commonwealth, and the country was a de facto republic led by Oliver Cromwell. Cromwell defeated Charles II at the Battle of Worcester on 3 September 1651, and Charles fled to mainland Europe. Cromwell became virtual dictator of England, Scotland and Ireland. Charles spent the next nine years in exile in France, the Dutch Republic and the Spanish Netherlands. The political crisis that followed Cromwell's death i ...
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Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science". Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to many eminent scientists throughout history, including Isaac Newton (1672), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Albert Einstein (1921), Paul Dirac (1930), Winston Churchill (1941), Subrahmanyan Chandrasekhar (1944), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955) and Francis Crick (1959). More recently, fellowship has been awarded to Stephen Hawking (1974), David Attenborough (1983), Tim Hunt (1991), Elizabeth Blackburn (1992), Tim Berners-Lee (2001), Venki Ramakrishn ...
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