1.
Merchiston Castle
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Merchiston Castle or Merchiston Tower was probably built by Alexander Napier, the second Laird of Merchiston around 1454. It serves as the seat for Clan Napier and it is perhaps most notable for being the home of John Napier, the 8th Laird of Merchiston, inventor of logarithms who was born there in 1550. The lands surrounding the castle were acquired in 1438 by Alexander Napier, the first Laird of Merchiston, and remained in the Napier family for most of the following five centuries. During restoration in the 1960s, a 26-pound cannonball was found embedded in the Tower, in 1659, the castle was sold to Ninian Lowis, in whose family it remained until 1729, when it was sold to the governors of George Watsons Hospital. The tower was reacquired by the Napier of Merchiston family when Francis Napier, in 1772, a year before the sixth Lords death, the Tower was sold to a relative, Charles Hope-Weir, second son of John Hope, 2nd Earl of Hopetoun. Weir sold it in 1775 to Robert Turner, a lawyer, who sold it in 1785 to Robert Blair, the Napier family again came into possession of Merchiston Castle in 1818, when it was purchased by William Napier, 9th Lord Napier. In 1833, Lord Napier let the Tower to Charles Chalmers and it was sold outright to the school in 1914 by The Honourable John Scott Napier, fourteenth Laird of Merchiston. The school vacated the building in 1930, moving to a site three miles away. In 1930 the property returned to the ownership of The Merchant Company, who used nearby playing fields for George Watsons College, then in 1935 the tower passed to Edinburgh City Council. It remained unoccupied until 1956, when it was suggested as the centrepiece of a new technical college, restoration work began in 1958, highlights of which were the discovery of the entrance drawbridge and the preservation of an original seventeenth-century plaster ceiling. It now stands at the centre of Napier University’s Merchiston campus, the Tower is an interesting and elaborate example of the medieval tower house, being built on the familiar L plan with a wing projecting to the north. It was originally vaulted at the floor and the roof. Among several remarkable features is the elaboration of the main entrance. The tall shallow recess in which the doorway is set undoubtedly housed a drawbridge which must have rested upon an outwork some 14 feet above ground level and 10 feet from the Tower. Shortly after being let to Merchiston Castle School it was altered with the addition of a castellated Gothic-style two-story extension and a basement. Napier University has taken out large sections of wall on the extension to accommodate a corridor which runs through the Castle to other campus buildings
2.
Edinburgh
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Edinburgh is the capital city of Scotland and one of its 32 local government council areas. Located in Lothian on the Firth of Forths southern shore, it is Scotlands second most populous city and the seventh most populous in the United Kingdom. The 2014 official population estimates are 464,990 for the city of Edinburgh,492,680 for the authority area. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is home to the Scottish Parliament and it is the largest financial centre in the UK after London. Historically part of Midlothian, the city has long been a centre of education, particularly in the fields of medicine, Scots law, literature, the sciences and engineering. The University of Edinburgh, founded in 1582 and now one of four in the city, was placed 17th in the QS World University Rankings in 2013 and 2014. The city is famous for the Edinburgh International Festival and the Fringe. The citys historical and cultural attractions have made it the United Kingdoms second most popular tourist destination after London, attracting over one million overseas visitors each year. Historic sites in Edinburgh include Edinburgh Castle, Holyrood Palace, the churches of St. Giles, Greyfriars and the Canongate, Edinburghs Old Town and New Town together are listed as a UNESCO World Heritage Site, which has been managed by Edinburgh World Heritage since 1999. It appears to derive from the place name Eidyn mentioned in the Old Welsh epic poem Y Gododdin, the poem names Din Eidyn as a hill fort in the territory of the Gododdin. The Celtic element din was dropped and replaced by the Old English burh, the first documentary evidence of the medieval burgh is a royal charter, c. 1124–1127, by King David I granting a toft in burgo meo de Edenesburg to the Priory of Dunfermline. In modern Gaelic, the city is called Dùn Èideann, the earliest known human habitation in the Edinburgh area was at Cramond, where evidence was found of a Mesolithic camp site dated to c.8500 BC. Traces of later Bronze Age and Iron Age settlements have found on Castle Rock, Arthurs Seat, Craiglockhart Hill. When the Romans arrived in Lothian at the end of the 1st century AD, at some point before the 7th century AD, the Gododdin, who were presumably descendants of the Votadini, built the hill fort of Din Eidyn or Etin. Although its location has not been identified, it likely they would have chosen a commanding position like the Castle Rock, Arthurs Seat. In 638, the Gododdin stronghold was besieged by forces loyal to King Oswald of Northumbria and it thenceforth remained under their jurisdiction. The royal burgh was founded by King David I in the early 12th century on land belonging to the Crown, in 1638, King Charles Is attempt to introduce Anglican church forms in Scotland encountered stiff Presbyterian opposition culminating in the conflicts of the Wars of the Three Kingdoms. In the 17th century, Edinburghs boundaries were defined by the citys defensive town walls
3.
Scotland
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Scotland is a country that is part of the United Kingdom and covers the northern third of the island of Great Britain. It shares a border with England to the south, and is surrounded by the Atlantic Ocean, with the North Sea to the east. In addition to the mainland, the country is made up of more than 790 islands, including the Northern Isles, the Kingdom of Scotland emerged as an independent sovereign state in the Early Middle Ages and continued to exist until 1707. By inheritance in 1603, James VI, King of Scots, became King of England and King of Ireland, Scotland subsequently entered into a political union with the Kingdom of England on 1 May 1707 to create the new Kingdom of Great Britain. The union also created a new Parliament of Great Britain, which succeeded both the Parliament of Scotland and the Parliament of England. Within Scotland, the monarchy of the United Kingdom has continued to use a variety of styles, titles, the legal system within Scotland has also remained separate from those of England and Wales and Northern Ireland, Scotland constitutes a distinct jurisdiction in both public and private law. Glasgow, Scotlands largest city, was one of the worlds leading industrial cities. Other major urban areas are Aberdeen and Dundee, Scottish waters consist of a large sector of the North Atlantic and the North Sea, containing the largest oil reserves in the European Union. This has given Aberdeen, the third-largest city in Scotland, the title of Europes oil capital, following a referendum in 1997, a Scottish Parliament was re-established, in the form of a devolved unicameral legislature comprising 129 members, having authority over many areas of domestic policy. Scotland is represented in the UK Parliament by 59 MPs and in the European Parliament by 6 MEPs, Scotland is also a member nation of the British–Irish Council, and the British–Irish Parliamentary Assembly. Scotland comes from Scoti, the Latin name for the Gaels, the Late Latin word Scotia was initially used to refer to Ireland. By the 11th century at the latest, Scotia was being used to refer to Scotland north of the River Forth, alongside Albania or Albany, the use of the words Scots and Scotland to encompass all of what is now Scotland became common in the Late Middle Ages. Repeated glaciations, which covered the land mass of modern Scotland. It is believed the first post-glacial groups of hunter-gatherers arrived in Scotland around 12,800 years ago, the groups of settlers began building the first known permanent houses on Scottish soil around 9,500 years ago, and the first villages around 6,000 years ago. The well-preserved village of Skara Brae on the mainland of Orkney dates from this period and it contains the remains of an early Bronze Age ruler laid out on white quartz pebbles and birch bark. It was also discovered for the first time that early Bronze Age people placed flowers in their graves, in the winter of 1850, a severe storm hit Scotland, causing widespread damage and over 200 deaths. In the Bay of Skaill, the storm stripped the earth from a large irregular knoll, when the storm cleared, local villagers found the outline of a village, consisting of a number of small houses without roofs. William Watt of Skaill, the laird, began an amateur excavation of the site, but after uncovering four houses
4.
University of St Andrews
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The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland, St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy. St Andrews is made up from a variety of institutions, including three constituent colleges and 18 academic schools organised into four faculties, the university occupies historic and modern buildings located throughout the town. The academic year is divided into two terms, Martinmas and Candlemas, in term time, over one-third of the towns population is either a staff member or student of the university. It is ranked as the third best university in the United Kingdom in national league tables, the Times Higher Education World Universities Ranking names St Andrews among the worlds Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom, St Andrews has many notable alumni and affiliated faculty, including eminent mathematicians, scientists, theologians, philosophers, and politicians. Six Nobel Laureates are among St Andrews alumni and former staff, a charter of privilege was bestowed upon the society of masters and scholars by the Bishop of St Andrews, Henry Wardlaw, on 28 February 1411. Wardlaw then successfully petitioned the Avignon Pope Benedict XIII to grant the university status by issuing a series of papal bulls. King James I of Scotland confirmed the charter of the university in 1432, subsequent kings supported the university with King James V confirming privileges of the university in 1532. A college of theology and arts called St Johns College was founded in 1418 by Robert of Montrose, St Salvators College was established in 1450, by Bishop James Kennedy. St Leonards College was founded in 1511 by Archbishop Alexander Stewart, St Johns College was refounded by Cardinal James Beaton under the name St Marys College in 1538 for the study of divinity and law. Some university buildings that date from this period are still in use today, such as St Salvators Chapel, St Leonards College Chapel, at this time, the majority of the teaching was of a religious nature and was conducted by clerics associated with the cathedral. During the 17th and 18th centuries, the university had mixed fortunes and was beset by civil. He described it as pining in decay and struggling for life, in the second half of the 19th century, pressure was building upon universities to open up higher education to women. In 1876, the University Senate decided to allow women to receive an education at St Andrews at a roughly equal to the Master of Arts degree that men were able to take at the time. The scheme came to be known as the L. L. A and it required women to pass five subjects at an ordinary level and one at honours level and entitled them to hold a degree from the university. In 1889 the Universities Act made it possible to admit women to St Andrews. Agnes Forbes Blackadder became the first woman to graduate from St Andrews on the level as men in October 1894
5.
Logarithm
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In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed number, in simple cases the logarithm counts factors in multiplication. For example, the base 10 logarithm of 1000 is 3, the logarithm of x to base b, denoted logb, is the unique real number y such that by = x. For example, log2 =6, as 64 =26, the logarithm to base 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the e as its base, its use is widespread in mathematics and physics. The binary logarithm uses base 2 and is used in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations and they were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the function in the 18th century. Logarithmic scales reduce wide-ranging quantities to tiny scopes, for example, the decibel is a unit quantifying signal power log-ratios and amplitude log-ratios. In chemistry, pH is a measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and they describe musical intervals, appear in formulas counting prime numbers, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithm reverses exponentiation, the logarithm is the inverse function of the exponential function applied to complex numbers. The discrete logarithm is another variant, it has uses in public-key cryptography, the idea of logarithms is to reverse the operation of exponentiation, that is, raising a number to a power. For example, the power of 2 is 8, because 8 is the product of three factors of 2,23 =2 ×2 ×2 =8. It follows that the logarithm of 8 with respect to base 2 is 3, the third power of some number b is the product of three factors equal to b. More generally, raising b to the power, where n is a natural number, is done by multiplying n factors equal to b. The n-th power of b is written bn, so that b n = b × b × ⋯ × b ⏟ n factors, exponentiation may be extended to by, where b is a positive number and the exponent y is any real number. For example, b−1 is the reciprocal of b, that is, the logarithm of a positive real number x with respect to base b, a positive real number not equal to 1, is the exponent by which b must be raised to yield x
6.
Napier's bones
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Napiers bones is a manually-operated calculating device created by John Napier of Merchiston for calculation of products and quotients of numbers. The method was based on Arab mathematics and the lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab, the technique was also called Rabdology. Napier published his version in 1617 in Rabdology, printed in Edinburgh, Scotland, dedicated to his patron Alexander Seton. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations, more advanced use of the rods can even extract square roots. Note that Napiers bones are not the same as logarithms, with which Napiers name is also associated, the complete device usually includes a base board with a rim, the user places Napiers rods inside the rim to conduct multiplication or division. The boards left edge is divided into 9 squares, holding the numbers 1 to 9, the Napiers rods consist of strips of wood, metal or heavy cardboard. Napiers bones are three-dimensional, square in section, with four different rods engraved on each one. A set of such bones might be enclosed in a convenient carrying case, a rods surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The digits of each product are written one to side of the diagonal, numbers less than 10 occupy the lower triangle. A set consists of 10 rods corresponding to digits 0 to 9, the rod 0, although it may look unnecessary, is needed for multipliers or multiplicands having 0 in them. To demonstrate how to use Napier’s Bones for multiplication, three examples of increasing difficulty are explained below, problem, Multiply 425 by 6 Start by placing the bones corresponding to the leading number of the problem into the boards. If a 0 is used in number, a space is left between the bones corresponding to where the 0 digit would be. In this example, the bones 4,2, and 5 are placed in the order as shown below. Looking at the first column, choose the number wishing to multiply by, in this example, that number is 6. The row this number is located in is the only row needed to perform the remaining calculations, starting at the right side of the row, evaluate the diagonal columns by adding the numbers that share the same diagonal column. Single numbers simply remain that number, once the diagonal columns have been evaluated, one must simply read from left to right the numbers calculated for each diagonal column. For this example, reading the results of the summations from left to right produces the answer of 2550. Therefore, The solution to multiplying 425 by 6 is 2550, when multiplying by larger single digits, it is common that upon adding a diagonal column, the sum of the numbers result in a number that is 10 or greater
7.
Decimal point
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A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for the decimal mark, the choice of symbol for the decimal mark also affects the choice of symbol for the thousands separator used in digit grouping, so the latter is also treated in this article. In mathematics the decimal mark is a type of radix point, in the Middle Ages, before printing, a bar over the units digit was used to separate the integral part of a number from its fractional part, e. g.9995. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear, a similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal mark, e. g.9995. Later, a separatrix between the units and tenths position became the norm among Arab mathematicians, e. g. 99ˌ95, when this character was typeset, it was convenient to use the existing comma or full stop instead. The separatrix was also used in England as an L-shaped or vertical bar before the popularization of the period, gerbert of Aurillac marked triples of columns with an arc when using his Hindu–Arabic numeral-based abacus in the 10th century. Fibonacci followed this convention when writing numbers such as in his influential work Liber Abaci in the 13th century, in France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen. Many other countries, such as Italy, also chose to use the comma to mark the decimal units position and it has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits, in some countries, a raised dot or dash may be used for grouping or decimal mark, this is particularly common in handwriting. In the United States, the stop or period was used as the standard decimal mark. g. However, as the mid dot was already in use in the mathematics world to indicate multiplication. In the event, the point was decided on by the Ministry of Technology in 1968, the three most spoken international auxiliary languages, Ido, Esperanto, and Interlingua, all use the comma as the decimal mark. Interlingua has used the comma as its decimal mark since the publication of the Interlingua Grammar in 1951, Esperanto also uses the comma as its official decimal mark, while thousands are separated by non-breaking spaces,12345678,9. Idos Kompleta Gramatiko Detaloza di la Linguo Internaciona Ido officially states that commas are used for the mark while full stops are used to separate thousands, millions. So the number 12,345,678.90123 for instance, the 1931 grammar of Volapük by Arie de Jong uses the comma as its decimal mark, and uses the middle dot as the thousands separator. In 1958, disputes between European and American delegates over the representation of the decimal mark nearly stalled the development of the ALGOL computer programming language. ALGOL ended up allowing different decimal marks, but most computer languages, the 22nd General Conference on Weights and Measures declared in 2003 that the symbol for the decimal marker shall be either the point on the line or the comma on the line. It further reaffirmed that numbers may be divided in groups of three in order to facilitate reading, neither dots nor commas are ever inserted in the spaces between groups
8.
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
9.
Henry Briggs (mathematician)
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Henry Briggs was an English mathematician notable for changing the original logarithms invented by John Napier into common logarithms, which are sometimes known as Briggsian logarithms in his honour. Briggs was a puritan and an influential professor in his time. He was born at Warleywood, near Halifax, in Yorkshire, after studying Latin and Greek at a local grammar school, he entered St Johns College, Cambridge, in 1577, and graduated in 1581. In 1588, he was elected of Fellow of St. Johns, in 1592 he was made reader of the physical lecture founded by Thomas Linacre, he would also read some of the mathematical lectures as well. During this period, he took an interest in navigation and astronomy, in 1596, he became first professor of Geometry in the recently founded Gresham College, London, where he taught geometry, astronomy and navigation. He would lecture there for nearly 23 years, and would make Gresham college a center of English mathematics and he was a friend of Christopher Heydon, the writer on astrology, though Briggs himself rejected astrology for religious reasons. At this time, Briggs obtained a copy of Mirifici Logarithmorum Canonis Descriptio, Briggs was active in many areas, and his advice in astronomy, surveying, navigation, and other activities like mining was frequently sought. Briggs in 1619 invested in the London Company, and he had two sons, Henry, who emigrated to Virginia, and Thomas, who remained in England. The lunar crater Briggs is named in his honour, in 1616 Briggs visited Napier at Edinburgh in order to discuss the suggested change to Napiers logarithms. The following year he visited for a similar purpose. During these conferences the alteration proposed by Briggs was agreed upon, in 1619 he was appointed Savilian professor of geometry at Oxford, and resigned his professorship of Gresham College in July 1620. Soon after his settlement at Oxford he was incorporated master of arts, in 1622 he published a small tract on the Northwest Passage to the South Seas, through the Continent of Virginia and Hudson Bay. The tract is notorious today as the origin of the myth of California as an Island. In it Briggs stated he had seen a map that had brought from Holland that showed California Island. Briggs tract was republished three years later in Pvrchas His Pilgrimes, in 1624 his Arithmetica Logarithmica, in folio, a work containing the logarithms of thirty thousand natural numbers to fourteen decimal places. This table was later extended by Adriaan Vlacq, but to 10 places, Briggs was one of the first to use finite-difference methods to compute tables of functions. Briggs discovered, in a concealed form and without proof. English translations of Briggss Arithmetica and the first part of his Trigonometria Britannica are available on the web, Briggs was buried in the chapel of Merton College, Oxford
10.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
11.
Physicist
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A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe. A physicist is a scientist who specializes or works in the field of physics, physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists can also apply their knowledge towards solving real-world problems or developing new technologies, some physicists specialize in sectors outside the science of physics itself, such as engineering. The study and practice of physics is based on a ladder of discoveries. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture and Asian culture, the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo and Kepler in the early 1600s. New knowledge in the early 21st century includes an increase in understanding physical cosmology. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences, many physicist positions require an undergraduate degree in applied physics or a related science or a Masters degree like MSc, MPhil, MPhys or MSci. In a research oriented level, students tend to specialize in a particular field, Physics students also need training in mathematics, and also in computer science and programming. For being employed as a physicist a doctoral background may be required for certain positions, undergraduate students like BSc Mechanical Engineering, BSc Electrical and Computer Engineering, BSc Applied Physics. etc. With physics orientation are chosen as research assistants with faculty members, the highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. The three major employers of career physicists are academic institutions, laboratories, and private industries, with the largest employer being the last, physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr. /Jr. As per the American Institute for Physics, some 20% of new physics Ph. D. s holds jobs in engineering development programs, while 14% turn to computer software, a majority of physicists employed apply their skills and training to interdisciplinary sectors. For industry or self-employment. and also in science and programming. Hence a majority of Physics bachelors degree holders are employed in the private sector, other fields are academia, government and military service, nonprofit entities, labs and teaching
12.
Astronomer
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An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside of the scope of Earth. They look at stars, planets, moons, comets and galaxies, as well as other celestial objects — either in observational astronomy. Examples of topics or fields astronomers work on include, planetary science, solar astronomy, there are also related but distinct subjects like physical cosmology which studies the Universe as a whole. Astronomers usually fit into two types, Observational astronomers make direct observations of planets, stars and galaxies, and analyze the data, theoretical astronomers create and investigate models of things that cannot be observed. They use this data to create models or simulations to theorize how different celestial bodies work, there are further subcategories inside these two main branches of astronomy such as planetary astronomy, galactic astronomy or physical cosmology. Today, that distinction has disappeared and the terms astronomer. Professional astronomers are highly educated individuals who typically have a Ph. D. in physics or astronomy and are employed by research institutions or universities. They spend the majority of their time working on research, although quite often have other duties such as teaching, building instruments. The number of astronomers in the United States is actually quite small. The American Astronomical Society, which is the organization of professional astronomers in North America, has approximately 7,000 members. This number includes scientists from other such as physics, geology. The International Astronomical Union comprises almost 10,145 members from 70 different countries who are involved in research at the Ph. D. level. Before CCDs, photographic plates were a method of observation. Modern astronomers spend relatively little time at telescopes usually just a few weeks per year, analysis of observed phenomena, along with making predictions as to the causes of what they observe, takes the majority of observational astronomers time. Astronomers who serve as faculty spend much of their time teaching undergraduate and graduate classes, most universities also have outreach programs including public telescope time and sometimes planetariums as a public service to encourage interest in the field. Those who become astronomers usually have a background in maths, sciences. Taking courses that teach how to research, write and present papers are also invaluable, in college/university most astronomers get a Ph. D. in astronomy or physics. Keeping in mind how few there are it is understood that graduate schools in this field are very competitive
13.
Laird
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Laird is a generic name for the owner of a large, long-named Scottish estate, roughly equivalent to an esquire in England, yet ranking above the same in Scotland. In the Scottish order of precedence, a laird ranks below a baron and this rank is only held by those lairds holding official recognition in a territorial designation by the Lord Lyon King of Arms. They are usually styled of, and are entitled to place The Much Honoured before their name. g. THE HOLDER IS THE LORD OF THE MANOR/LAIRD OF and it is a description rather than a title, and is not appropriate for the owner of a normal residential property, far less the owner of a small souvenir plot of land. It goes without saying that the term ‘laird’ is not synonymous with that of ‘lord’ or ‘lady’, ownership of a souvenir plot of land is not sufficient to bring a person otherwise ineligible within the jurisdiction of the Lord Lyon for the purpose of seeking a Grant of Arms. Historically, the bonnet laird was applied to rural, petty landowners. Bonnet lairds filled a position in society below lairds and above husbandmen, the word laird is known to have been used from the 15th century, and is a shortened form of laverd, derived from the Old English word hlafweard meaning warden of loaves. In the 15th and 16th centuries, the designation was used for land owners holding directly of the Crown, lairds reigned over their estates like princes, their castles forming a small court. Originally in the 16th and 17th centuries, the designation was applied to the chief of a highland clan. The laird may possess certain local or feudal rights, a certain level of landownership was a necessary qualification. A laird is said to hold a lairdship, a woman who holds a lairdship in her own right has been styled with the honorific Lady. Although laird is sometimes translated as lord and historically signifies the same, the designation is a corporeal hereditament, i. e. the designation cannot be held in gross, and cannot be bought and sold without selling the physical land. A laird possessing a Coat of Arms registered in the Public Register of All Arms, several websites, and internet vendors on websites like Ebay, sell Scottish lairdships along with small plots of land. They see their contract purporting to sell a plot of Scottish souvenir land as bestowing them the right to the title Laird. This is despite the fact that the buyer does not acquire ownership of the plot because registration of the plot is prohibited by Land Registration Act 2012, s 22. While tolerating public access, he feels threatened by new legislation, traditionally, a laird is formally styled in the manner evident on the 1730 tombstone in a Scottish churchyard. It reads, The Much Honoured Laird of, the section titled Scottish Feudal Baronies in Debretts states that the use of the prefix The Much Hon. is correct, but that most lairds prefer the unadorned name and territorial designation. By the early 20th century, the wife came to adopt her husbands full surname
14.
Merchiston
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Merchiston is a prosperous, mainly residential area in the south-west of Edinburgh, Scotland. A campus forming a part of Edinburgh Napier University is in the area, it includes Merchiston Tower, once the home of John Napier, 8th Laird of Merchiston. The area is home to writers Ian Rankin, Lin Anderson, Colin Douglas, Alexander McCall Smith, rowling had her Edinburgh home in Merchiston for many years but is said to have moved to Cramond. Merchiston was also the home of Scotland and British Lions rugby legends Gavin Hastings. Also in the area are a number of independent schools including George Watsons College, on the fringes of the area where it meets Craiglockhart is the suburban railway line, which is mooted for reopening. To the north of the area is the Union Canal, other nearby areas include Morningside to the southeast, Burghmuirhead to the east and Bruntsfield to the northeast. Entry in Gazetteer for Scotland Merchiston Community Council Community Council map showing boundary of area Craiglockhart Primary School
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Edinburgh Napier University
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Edinburgh Napier University is a public university in Edinburgh, Scotland. It has over 19,500 students, including those on-campus in Scotland and others studying on transnational programmes abroad, in 2016 this included nearly 9,500 international and EU students, from more than 140 nations worldwide. His statue stands in the tower of Merchiston Castle today, in 1966, it was renamed Napier College of Science and Technology. In 1974, it merged with the Sighthill-based Edinburgh College of Commerce to form Napier College of Commerce and Technology, the college was renamed Napier Polytechnic in 1986 and in the same year acquired the former Hydropathic hospital buildings at Craiglockhart. In June 1992 the institution officially became Napier University, at a ceremony witnessed by over 700 staff and students, Lord James Douglas Hamilton and the then Principal, Professor William Turmeau, unveiled the new University sign at Merchiston. In 1994, Napier University acquired its Craighouse Campus, in 1996, the university gained a new Faculty of Health Studies through a merger between the Scottish Borders College of Nursing and Lothian College of Health Studies. In February 2009 it became Edinburgh Napier University Edinburgh Napier has been awarded the Queens Anniversary Prize twice and its most recent win came in 2015, when it was recognised for its work in timber engineering, sustainable construction and wood science. Edinburgh Napier was previously awarded the Queens Anniversary Prize in 2009 when the award was made for Innovative housing construction for environmental benefit and this recognised the contribution made by the Universitys Building Performance Centre towards improving sound insulation between attached dwellings. The motto of the University, Nisi sapientia frustra, echoes the motto of the City of Edinburgh, Edinburgh Napiers Tartan was launched at the same time as the name change in February 2009. Previously the university used the Clan Napier Tartan, the Chief of Clan Napier welcomed the new University tartan, the university is based around its three main campuses at Merchiston, Craiglockhart and Sighthill. The Sighthill Campus opened to students in the School of Health & Social Care, the campus has received the BREEAM excellence rating. This sets the standard for best practice in sustainable design, in 2016, the gym facilities at Sighthill became home to the BT Sport Scottish Rugby Academy Edinburgh. The Craiglockhart Campus is home to The Business School, the Craiglockhart Campus exhibits photography, writing, film and memorabilia to provide a glimpse into the minds of the poets, patients and medical staff at Craiglockhart. The exhibition also provides War Poets Collection based on the work of Siegfried Sassoon, Wilfred Owen, the exhibition was officially opened on 11 November 2005 by BBCs World Affairs Correspondent, Allan Little. This campus is the home of the law and business courses and is also operates as a conference centre, the Craiglockhart Campus was refurbished in 2004 and contains two lecture theatres, language labs and computing facilities. The Merchiston Campus is home to the Schools of Art & Creative Industries and it is built around the refurbished shell of Merchiston Castle, the family home of John Napier, after whom the University is named. Merchiston Castle is also the ancient seat of Clan Napier, Merchiston Castle is currently a Category A listed building in Scotland due to its national significance. The campus also includes the 500-seat, 24-hour Jack Kilby Computing Centre, named after the inventor of integrated circuits, Edinburgh Napier Students Association is located at the Merchiston Campus
16.
High Kirk of St Giles
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St Giles Cathedral, also known as the High Kirk of Edinburgh, is the principal place of worship of the Church of Scotland in Edinburgh. Its distinctive crown steeple is a prominent feature of the city skyline, the church has been one of Edinburghs religious focal points for approximately 900 years. The present church dates from the late 14th century, though it was restored in the 19th century. Today it is regarded as the Mother Church of Presbyterianism. The cathedral is dedicated to Saint Giles, who is the saint of Edinburgh, as well as of cripples and lepers. It is the Church of Scotland parish church for part of Edinburghs Old Town, St Giles was only a cathedral in its formal sense for two periods during the 17th century, when episcopalianism, backed by the Crown, briefly gained ascendancy within the Kirk. In the mediaeval period, prior to the Reformation, Edinburgh had no cathedral as it was under the jurisdiction of the Bishop of St Andrews, for most of its post-Reformation history the Church of Scotland has not had bishops, dioceses, or cathedrals. As such, the use of the cathedral today carries no practical meaning. The High Kirk title is older, being attested well before the brief period as a cathedral. The oldest parts of the building are four central pillars, often said to date from 1124. In 1385 the building suffered a fire and was rebuilt in the subsequent years, much of the current interior dates from this period. Over the years many chapels, referred to as aisles, were added, greatly enlarging the church, in 1466 St Giles was established as a collegiate church by Pope Paul II. In response to this raising of status, the tower was added around 1490, and the chancel ceiling raised, vaulted. At the height of the Scottish Reformation the Protestant leader and firebrand John Knox was chosen minister at St Giles by Edinburgh Town Council, a 19th-century stained glass window in the south wall of the church shows him delivering the funeral sermon for the Regent Moray in 1570. A bronze statue of Knox, cast by Pittendrigh MacGillivray in 1904, by about 1580, the church was partitioned into separate preaching halls to suit the style of reformed Presbyterian worship for congregations drawn from the quarters of Edinburgh. The partition walls were removed in 1633 when St Giles became the cathedral for the new see of Edinburgh. Our pleasure is that with all diligence you cause raze to the ground the east wall in the church. The internal partitions were restored in 1639 and, after several re-arrangements, the disturbances led to the National Covenant and hence the Bishops Wars, the first conflicts of the Wars of the Three Kingdoms, which included the English Civil War
17.
Parliament House, Edinburgh
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For the building that houses the modern Scottish Parliament, see Scottish Parliament Building. Parliament House in Edinburgh, Scotland, was home to the pre-Union Parliament of Scotland and it is located in the Old Town, just off the Royal Mile, beside St Giles Cathedral. It was completed in 1639 to the design of James Murray and it has a dramatic hammer-beam roof constructed of oak from the Balgonie and Culross forests of Fife, thought to be the hardest and most durable in Scotland during that period. The roof of the former Tron Church in the High Street is similar, the roof of the new Scottish Parliament Building continues this tradition, and is supported by large laminated oak beams. After the Act of Union 1707, the Estates of Parliament was adjourned, the Hall was used for the sitting of courts, but in recent times has been subject to restoration work and now remains open as a meeting place for lawyers. Beneath Parliament Hall lies the Laigh Hall, of similar plan form, the right-hand example of the two smaller fireplaces has carved scenes from The Merchant of Venice. Statues on the wall include, The 1st Viscount Melville by Sir Francis Chantrey, The 2nd Viscount Melville by Sir Francis Chantrey. On the east wall, Duncan Forbes by Roubiliac, Lord Jeffrey by Sir John Steell, Lord President Boyle by Sir John Steell, Lord President Blair by Sir Francis Chantrey. On the west wall, Sir Walter Scott by John Greenshields, Henry Erskine by Peter Turnerelli, and various busts by William Brodie and Sir John Steell. There are multiple paintings by Sir Henry Raeburn, George Joseph Bell, Sir William Nairne, Lord Dunsinane, William Craig, Lord Craig, Matthew Ross, and Lord Abercromby of Tullibody. Paintings by John Watson Gordon include Lord Robertson, Alexander Wood, General Boyle and Erskine Douglas Sandford. in a corridor beyond the south door of the hall stand figures of Justice and Mercy by Alexander Mylne which formerly stood over the main entrance on Parliament Square. Even while the old Parliament was still in existence, parts of the buildings were used for legal cases, the building is now used to house the College of Justice and other connected functions. The Advocates Library was founded in 1682, and is located in a William Henry Playfair-designed building to the west of the south end of Parliament Hall. It remains a heavily used legal resource, to the west of the north end of Parliament Hall is The Signet Library. It is a library, funded by members of The Society of Writers to Her Majestys Signet. Construction began in 1810 to a design by Robert Reid, and this façade wraps around Parliament House as well, and replaced the existing Scottish baronial façade. Scots law Courts of Scotland Edinburgh City Chambers
18.
Sir Archibald Napier
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Sir Archibald Napier was a Scottish landowner and official, master of the Scottish mint and seventh Laird of Merchiston. He was eldest son of Alexander Napier, sixth of Merchiston and his mother was Annabella, youngest daughter of Sir Duncan Campbell of Glenurchy. His paternal grandfather was Sir Alexander, fifth of Merchiston, who was killed at the battle of Flodden in 1513, Napier began to clear his property of encumbrances. In 1565 he received the order of knighthood and he seems to have sided with Mary Queen of Scots after her escape from Lochleven Castle. On this account the defenders of the made a attempt to burn it. Napiers name appears with others in a contract with the regent for working for the space of twelve years certain gold, silver, copper, and lead mines. He was appointed general of the cunzie-house in 1576, and on 25 April 1581 he was directed, with others, to take proceedings against John Achesoun, in May 1580 he received payment for the expenses of a mission to England. On 6 March 1590 Napier was appointed one of a commission for putting Acts in force against the Jesuits. On account of non-appearance before the council of his son Alexander, charged with a serious assault, in September 1604 he went to London to treat with English commissioners about the Mint, when, according to Sir James Balfour, he negotiated skillfully. Napier continued till the end of his life to take a part in matters connected with mining. On 14 January 1608 he was appointed along with two others to repair to the mines in succession to try the quality of the ore and he died on 15 May 1608, aged 74. On 8 February 1588 the king granted to Napier, Elizabeth Mowbray, his wife, and Alexander, their son and heir. On 16 November 1593 he obtained a grant of half the lands of Lauriston, attribution This article incorporates text from a publication now in the public domain, Napier, Archibald
19.
Bishop of Orkney
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The Bishop of Orkney was the ecclesiastical head of the Diocese of Orkney, one of thirteen medieval bishoprics of Scotland. It included both Orkney and Shetland and it was based for almost all of its history at St. Magnus Cathedral, Kirkwall. The bishopric appears to have been suffragan of the Archbishop of York until the creation of the Archbishopric of Trondheim in 1152, although Orkney itself did not unite with mainland Scotland until 1468, the Scottish kings and political community had been pushing for control of the islands for centuries. The see, however, remained under the control of Trondheim until the creation of the Archbishopric of St. Andrews in 1472. The Bishoprics links with Rome ceased to exist after the Scottish Reformation, the bishopric continued, saving temporary abolition between 1638 and 1661, under the episcopal Church of Scotland until the Glorious Revolution of 1688. A Scottish Episcopal Church bishopric encompassing Orkney was created in 1865, as the Bishopric of Aberdeen and Orkney. Dowden, John, The Bishops of Scotland, ed. J. Maitland Thomson, Keith, Robert, An Historical Catalogue of the Scottish Bishops, Down to the Year 1688, Watt, fasti Ecclesiae Scotinanae Medii Aevi ad annum 1638, 2nd Draft
20.
St Salvator's College, St Andrews
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St Salvators College was a college of the University of St Andrews in St Andrews, Scotland. Founded in 1450, it is the oldest of the Universitys colleges, in 1747 it merged with St Leonards College to form United College. St Salvators College was founded in 1450 by Bishop James Kennedy, in 1528, the Protestant martyr, Patrick Hamilton, was burned alive outside the college, though Patrick himself was a member of St Leonards college. Initially a college of Theology and the Arts, St Salvators was created to revitalize, shortly after this, the initial site of St Leonards College was sold, though the university retained ownership of St Leonards College Chapel. Although the buildings of St Salvators College were grand by medieval standards, from 1837 the quadrangle was rebuilt and extended into its current form, with a north and a west wing in Jacobean style. To the south is the Chapel, where many university services are held, St Salvators College was residential until the unification with St Leonards. The current St Salvators Hall, which lies east of the college, is one of the halls of residence for students, the chapel, tower and Hebdomadars Building are all designated as Category A listed buildings by Historic Scotland. Other buildings and structures are listed as Category B, the college chapel is unusual for a collegiate church in that the main entrance faces out into the town, and not like those in Oxford or Cambridge, closed into the college itself. It is indeed the only chapel in Scotland with this arrangement. The chapel was used as a church after the St Leonards college chapel was unroofed in the 1750s until this arrangement was withdrawn by the university. The 1450 college had cloister buildings to the north of the college chapel - the two doors to the side of the chapel show the alignment of the cloister. It is commonly referred to as “the quad”, and is the setting of Raisin Monday festivities, the point of the post-Graduation processions. Cant The University of St. Andrews, A Short History
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France
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France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established. The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural, political, and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and later dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity. In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is also a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks
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Flanders
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Flanders is the Dutch-speaking northern portion of Belgium, although there are several overlapping definitions, including ones related to culture, language, politics and history. It is one of the communities, regions and language areas of Belgium, the demonym associated with Flanders is Fleming, while the corresponding adjective is Flemish. The official capital of Flanders is Brussels, although Brussels itself has an independent regional government, in historical contexts, Flanders originally refers to the County of Flanders, which around AD1000 stretched from the Strait of Dover to the Scheldt estuary. In accordance with late 20th century Belgian state reforms the area was made two political entities, the Flemish Community and the Flemish Region. These entities were merged, although geographically the Flemish Community, which has a cultural mandate, covers Brussels. Flanders has figured prominently in European history, as a consequence, a very sophisticated culture developed, with impressive achievements in the arts and architecture, rivaling those of northern Italy. Belgium was one of the centres of the 19th century industrial revolution, geographically, Flanders is generally flat, and has a small section of coast on the North Sea. Much of Flanders is agriculturally fertile and densely populated, with a density of almost 500 people per square kilometer. It touches France to the west near the coast, and borders the Netherlands to the north and east, the Brussels Capital Region is an enclave within the Flemish Region. Flanders has exclaves of its own, Voeren in the east is between Wallonia and the Netherlands and Baarle-Hertog in the consists of 22 exclaves surrounded by the Netherlands. It comprises 6.5 million Belgians who consider Dutch to be their mother tongue, the political subdivisions of Belgium, the Flemish Region and the Flemish Community. The first does not comprise Brussels, whereas the latter does comprise the Dutch-speaking inhabitants of Brussels, the political institutions that govern both subdivisions, the operative body Flemish Government and the legislative organ Flemish Parliament. The two westernmost provinces of the Flemish Region, West Flanders and East Flanders, forming the central portion of the historic County of Flanders, a feudal territory that existed from the 8th century until its absorption by the French First Republic. Until the 1600s, this county also extended over parts of France, one of the regions conquered by the French in Flanders, namely French Flanders in the Nord department. French Flanders can be divided into two regions, Walloon Flanders and Maritime Flanders. The first region was predominantly French-speaking already in the 1600s, the latter became so in the 20th century, the city of Lille identifies itself as Flemish, and this is reflected, for instance, in the name of its local railway station TGV Lille Flandres. The region conquered by the Dutch Republic in Flanders, now part of the Dutch province of Zeeland, the significance of the County of Flanders and its counts eroded through time, but the designation remained in a very broad sense. In the Early modern period, the term Flanders was associated with the part of the Low Countries
23.
Gartness, Stirling
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Gartness is a hamlet in Stirling, Scotland. It is located 1.8 miles/2.9 km from Killearn and 3.1 miles/5 km from Drymen, most pupils attend Killearn Primary School and senior pupils attend Balfron High School. The Endrick Water passes through the hamlet, in 1572, John Napier had an estate at Gartness with his second wife, Agnes Chisholm. The name derives from the Scottish Gaelic Gart an Easa, which means enclosed field by the stream, whilst the hamlet has no facilities, there is a gift shop located just outside the hamlet, the Wishingwell. Vision of Britain - Gartness Canmore - Gartness Castle Caledonian Mercury - The Pots of Gartness
24.
Napier's Bones
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Napiers bones is a manually-operated calculating device created by John Napier of Merchiston for calculation of products and quotients of numbers. The method was based on Arab mathematics and the lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab, the technique was also called Rabdology. Napier published his version in 1617 in Rabdology, printed in Edinburgh, Scotland, dedicated to his patron Alexander Seton. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations, more advanced use of the rods can even extract square roots. Note that Napiers bones are not the same as logarithms, with which Napiers name is also associated, the complete device usually includes a base board with a rim, the user places Napiers rods inside the rim to conduct multiplication or division. The boards left edge is divided into 9 squares, holding the numbers 1 to 9, the Napiers rods consist of strips of wood, metal or heavy cardboard. Napiers bones are three-dimensional, square in section, with four different rods engraved on each one. A set of such bones might be enclosed in a convenient carrying case, a rods surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The digits of each product are written one to side of the diagonal, numbers less than 10 occupy the lower triangle. A set consists of 10 rods corresponding to digits 0 to 9, the rod 0, although it may look unnecessary, is needed for multipliers or multiplicands having 0 in them. To demonstrate how to use Napier’s Bones for multiplication, three examples of increasing difficulty are explained below, problem, Multiply 425 by 6 Start by placing the bones corresponding to the leading number of the problem into the boards. If a 0 is used in number, a space is left between the bones corresponding to where the 0 digit would be. In this example, the bones 4,2, and 5 are placed in the order as shown below. Looking at the first column, choose the number wishing to multiply by, in this example, that number is 6. The row this number is located in is the only row needed to perform the remaining calculations, starting at the right side of the row, evaluate the diagonal columns by adding the numbers that share the same diagonal column. Single numbers simply remain that number, once the diagonal columns have been evaluated, one must simply read from left to right the numbers calculated for each diagonal column. For this example, reading the results of the summations from left to right produces the answer of 2550. Therefore, The solution to multiplying 425 by 6 is 2550, when multiplying by larger single digits, it is common that upon adding a diagonal column, the sum of the numbers result in a number that is 10 or greater
25.
Natural logarithm
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The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is written as ln x, loge x, or sometimes, if the base e is implicit. Parentheses are sometimes added for clarity, giving ln, loge or log and this is done in particular when the argument to the logarithm is not a single symbol, to prevent ambiguity. The natural logarithm of x is the power to which e would have to be raised to equal x. The natural log of e itself, ln, is 1, because e1 = e, while the natural logarithm of 1, ln, is 0, since e0 =1. The natural logarithm can be defined for any real number a as the area under the curve y = 1/x from 1 to a. The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, like all logarithms, the natural logarithm maps multiplication into addition, ln = ln + ln . However, logarithms in other bases differ only by a constant multiplier from the natural logarithm, for instance, the binary logarithm is the natural logarithm divided by ln, the natural logarithm of 2. Logarithms are useful for solving equations in which the unknown appears as the exponent of some other quantity, for example, logarithms are used to solve for the half-life, decay constant, or unknown time in exponential decay problems. They are important in many branches of mathematics and the sciences and are used in finance to solve problems involving compound interest, by Lindemann–Weierstrass theorem, the natural logarithm of any positive algebraic number other than 1 is a transcendental number. The concept of the natural logarithm was worked out by Gregoire de Saint-Vincent and their work involved quadrature of the hyperbola xy =1 by determination of the area of hyperbolic sectors. Their solution generated the requisite hyperbolic logarithm function having properties now associated with the natural logarithm, the notations ln x and loge x both refer unambiguously to the natural logarithm of x. log x without an explicit base may also refer to the natural logarithm. This usage is common in mathematics and some scientific contexts as well as in many programming languages, in some other contexts, however, log x can be used to denote the common logarithm. Historically, the notations l. and l were in use at least since the 1730s, finally, in the twentieth century, the notations Log and logh are attested. The graph of the logarithm function shown earlier on the right side of the page enables one to glean some of the basic characteristics that logarithms to any base have in common. Chief among them are, the logarithm of the one is zero. What makes natural logarithms unique is to be found at the point where all logarithms are zero. At that specific point the slope of the curve of the graph of the logarithm is also precisely one
26.
Napierian logarithm
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The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him, note that 16.11809565 ≈7 ln and 23025850 ≈107 ln . For further detail, see history of logarithms, a History of Mathematics, Wiley, p.313, ISBN 978-0-471-54397-8. Edwards, Charles Henry, The Historical Development of the Calculus, Springer-Verlag, phillips, George McArtney, Two Millennia of Mathematics, from Archimedes to Gauss, CMS Books in Mathematics,6, Springer-Verlag, p.61, ISBN 978-0-387-95022-8. Denis Roegel Napier’s Ideal Construction of the Logarithms, from the Loria Collection of Mathematical Tables
27.
Spherical trigonometry
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Spherical trigonometry is of great importance for calculations in astronomy, geodesy and navigation. The origins of spherical trigonometry in Greek mathematics and the developments in Islamic mathematics are discussed fully in History of trigonometry. This book is now available on the web. The only significant developments since then have been the application of methods for the derivation of the theorems. A spherical polygon is a polygon on the surface of the sphere defined by a number of great-circle arcs, such polygons may have any number of sides. Two planes define a lune, also called a digon or bi-angle, the analogue of the triangle. Three planes define a triangle, the principal subject of this article. Four planes define a spherical quadrilateral, such a figure, and higher sided polygons, from this point the article will be restricted to spherical triangles, denoted simply as triangles. Both vertices and angles at the vertices are denoted by the upper case letters A, B and C. The angles of spherical triangles are less than π so that π < A + B + C < 3π. The sides are denoted by letters a, b, c. On the unit sphere their lengths are equal to the radian measure of the angles that the great circle arcs subtend at the centre. The sides of proper spherical triangles are less than π so that 0 < a + b + c < 3π, the radius of the sphere is taken as unity. For specific practical problems on a sphere of radius R the measured lengths of the sides must be divided by R before using the identities given below, likewise, after a calculation on the unit sphere the sides a, b, c must be multiplied by R. The polar triangle associated with a triangle ABC is defined as follows, consider the great circle that contains the side BC. This great circle is defined by the intersection of a plane with the surface. The points B and C are defined similarly, the triangle ABC is the polar triangle corresponding to triangle ABC. Therefore, if any identity is proved for the triangle ABC then we can derive a second identity by applying the first identity to the polar triangle by making the above substitutions
28.
Gresham College
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Gresham College is an institution of higher learning located at Barnards Inn Hall off Holborn in central London, England. It was founded in 1597 under the will of Sir Thomas Gresham, the College remained in Greshams mansion in Bishopsgate until 1768, and moved about London thereafter until the construction in 1842 of its own buildings in Gresham Street EC2. Since 1991, the College has operated at Barnard’s Inn Hall, early distinguished Gresham College professors included Christopher Wren, who lectured on astronomy in the 17th century and Robert Hooke, who was Professor of Geometry from 1665 until 1704. Today three further Professorships have been added to account of areas not otherwise covered by the original Professorships, Commerce. The professors currently hold their positions for three years, extendable for a year, and give six lectures a year. There are also regular visiting professors appointed to give series of lectures at the College, since 2000, the college regularly welcomes visiting speakers who deliver lectures on topics outside its usual range, and it also hosts occasional seminars and conferences. Today the college provides in the region of 130 lectures a year, all of which are free, although many of the lectures are held in Barnard’s Inn Hall, the majority are now held in the lecture hall at the Museum of London, for reasons of capacity. Since 2001, the college has been recording its lectures and releasing them online in what is now an archive of over 2,000 lectures. Annual lectures of particular note hosted by the college include, the Gresham Special Lecture, the Annual Lord Mayor’s Event, the College does not enroll any students and awards no degrees. The Gresham Special Lecture originated in 1988 as a public lecture delivered by a prominent speaker. It was devised as a focus-point among the other 126 free public lectures offered every year,2012, The Rt Hon John Bercow – Parliament and the Public, Strangers or Friends. AND I will and dispose, that, the said maior and corporation of the said cittye. Hellynes in Bishopsgate streete and St. Peeters the pore in the cittye of London. The somme of two hundred pounds of money of England, in manner and forme followinge, viz. Mary the Virgin and of St. Mighell tharchangell. Hellyns in Bishopesgate streete and St. Peters the pore, in the cittye of London. The somme of one hundred and fifty poundes of lawfull money of England, in manner and forme followinge, viz. Mighell the Archangell, by even portions to be paid. Thomas Greshams mansion converted into a facility with lodgings and research space for professors of Law, Physics, Music, Divinity, Geometry, Rhetoric. By me THOMAS GRESHAM Witnesses to this last will and testament of the said Sir Thomas Gresham the persons whose names be subscribed, PH
29.
Exponential notation
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Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations, on scientific calculators it is known as SCI display mode. In scientific notation all numbers are written in the form m × 10n, where the exponent n is an integer, however, the term mantissa may cause confusion because it is the name of the fractional part of the common logarithm. If the number is then a minus sign precedes m. In normalized notation, the exponent is chosen so that the value of the coefficient is at least one. Decimal floating point is an arithmetic system closely related to scientific notation. Any given integer can be written in the form m×10^n in many ways, in normalized scientific notation, the exponent n is chosen so that the absolute value of m remains at least one but less than ten. Thus 350 is written as 3. 5×102 and this form allows easy comparison of numbers, as the exponent n gives the numbers order of magnitude. In normalized notation, the exponent n is negative for a number with absolute value between 0 and 1, the 10 and exponent are often omitted when the exponent is 0. Normalized scientific form is the form of expression of large numbers in many fields, unless an unnormalized form. Normalized scientific notation is often called exponential notation—although the latter term is general and also applies when m is not restricted to the range 1 to 10. Engineering notation differs from normalized scientific notation in that the exponent n is restricted to multiples of 3, consequently, the absolute value of m is in the range 1 ≤ |m| <1000, rather than 1 ≤ |m| <10. Though similar in concept, engineering notation is rarely called scientific notation, engineering notation allows the numbers to explicitly match their corresponding SI prefixes, which facilitates reading and oral communication. A significant figure is a digit in a number that adds to its precision and this includes all nonzero numbers, zeroes between significant digits, and zeroes indicated to be significant. Leading and trailing zeroes are not significant because they exist only to show the scale of the number. Therefore,1,230,400 usually has five significant figures,1,2,3,0, and 4, when a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required, thus 1,230,400 would become 1.2304 ×106. However, there is also the possibility that the number may be known to six or more significant figures, thus, an additional advantage of scientific notation is that the number of significant figures is clearer
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Astronomy
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Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, physics, and chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, moons, stars, galaxies, and comets, while the phenomena include supernovae explosions, gamma ray bursts, more generally, all astronomical phenomena that originate outside Earths atmosphere are within the purview of astronomy. A related but distinct subject, physical cosmology, is concerned with the study of the Universe as a whole, Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as the Babylonians, Greeks, Indians, Egyptians, Nubians, Iranians, Chinese, during the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can play an active role, especially in the discovery. Amateur astronomers have made and contributed to many important astronomical discoveries, Astronomy means law of the stars. Astronomy should not be confused with astrology, the system which claims that human affairs are correlated with the positions of celestial objects. Although the two share a common origin, they are now entirely distinct. Generally, either the term astronomy or astrophysics may be used to refer to this subject, however, since most modern astronomical research deals with subjects related to physics, modern astronomy could actually be called astrophysics. Few fields, such as astrometry, are purely astronomy rather than also astrophysics, some titles of the leading scientific journals in this field includeThe Astronomical Journal, The Astrophysical Journal and Astronomy and Astrophysics. In early times, astronomy only comprised the observation and predictions of the motions of objects visible to the naked eye, in some locations, early cultures assembled massive artifacts that possibly had some astronomical purpose. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye, most of early astronomy actually consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, and the nature of the Sun, Moon, the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the model of the Universe, or the Ptolemaic system. The Babylonians discovered that lunar eclipses recurred in a cycle known as a saros
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Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
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Simon Stevin
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Simon Stevin, sometimes called Stevinus, was a Flemish/Dutch/Netherlandish mathematician, physicist and engineer. He was active in a great areas of science and engineering. Very little is known with certainty about Stevins life and what we know is mostly inferred from other recorded facts, the exact birth date and the date and place of his death are uncertain. It is assumed he was born in Bruges since he enrolled at Leiden University under the name Simon Stevinus Brugensis and his name is usually written as Stevin, but some documents regarding his father use the spelling Stevijn. This is a normal spelling shift in 16th century Dutch and he was born around the year 1548 to unmarried parents, Anthonis Stevin and Catelyne van der Poort. His father is believed to have been a son of a mayor of Veurne. While Simons father was not mentioned in the book of burghers, many other Stevins were later mentioned in the Poorterboeken. Simon Stevins mother Cathelijne was the daughter of a family from Ypres. Her father Hubert was a poorter of Bruges, Simons mother Cathelijne later married Joost Sayon who was involved in the carpet and silk trade and a member of the schuttersgilde Sint-Sebastiaan. Through her marriage Cathelijne became a member of a family of Calvinists and it is believed that Stevin grew up in a relatively affluent environment and enjoyed a good education. He was likely educated at a Latin school in his hometown, Stevin left Bruges in 1571 apparently without a particular destination. Stevin was most likely a Calvinist since a Catholic would likely not have risen to the position of trust he later occupied with Maurice, Prince of Orange and it is assumed that he left Bruges to escape the religious persecution of Protestants by the Spanish rulers. Based on references in his work Wisconstighe Ghedaechtenissen, it has been inferred that he must have moved first to Antwerp where he began his career as a merchants clerk. Some biographers mention that he travelled to Prussia, Poland, Denmark, Norway and Sweden and other parts of Northern Europe and it is possible that he completed these travels over a longer period of time. In 1577 Simon Stevin returned to Bruges and was appointed city clerk by the aldermen of Bruges and he worked in the office of Jan de Brune of the Brugse Vrije, the castellany of Bruges. Why he had returned to Bruges in 1577 is not clear and it may have been related to the political events of that period. Bruges was the scene of religious conflict. Catholics and Calvinists alternately controlled the government of the city and they usually opposed each other but would occasionally collaborate in order to counteract the dictates of King Philip II of Spain
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Lattice multiplication
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It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use. The method had already arisen by medieval times, and has used for centuries in many different cultures. It is still being taught in certain curricula today, a grid is drawn up, and each cell is split diagonally. Then each cell of the lattice is filled in with product of its column, as an example, lets consider the multiplication of 58 with 213. After writing the multiplicands on the sides, consider each cell, in this case, the column digit is 5 and the row digit is 2. Write their product,10, in the cell, with the digit 1 above the diagonal, if the simple product lacks a digit in the tens place, simply fill in the tens place with a 0. After all the cells are filled in this manner, the digits in each diagonal are summed, each diagonal sum is written where the diagonal ends. If the sum contains more than one digit, the value of the place is carried into the next diagonal. Numbers are filled to the left and to the bottom of the grid, the lattice technique can also be used to multiply decimal fractions. For instance, to multiply 5.8 by 2.13, a line could be drawn straight down from the decimal in 5.8. The lines are extended until they intersect, at which point they merge, the positioning of this diagonal line in the final result is the location of the decimal point. Lattice multiplication has been used historically in different cultures. It is not known where it arose first, nor whether it developed independently more than one region of the world. 1300 in Chinese mathematics was by Wu Jing in his Jiuzhang suanfa bilei daquan, the mathematician and educator David Eugene Smith asserted that lattice multiplication was brought to Italy from the Middle East. This is reinforced by noting that the Arabic term for the method, shabakh, has the meaning as the Italian term for the method, gelosia, namely. It is sometimes stated that lattice multiplication was described by Muḥammad ibn Mūsā al-Khwārizmī or by Fibonacci in his Liber Abaci. In fact, however, no use of multiplication by either of these two authors has been found. In Chapter 3 of his Liber Abaci, Fibonacci does describe a technique of multiplication by what he termed quadrilatero in forma scacherii
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Fibonacci
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Fibonacci was an Italian mathematician, considered to be the most talented Western mathematician of the Middle Ages. The name he is called, Fibonacci, is short for figlio di Bonacci and he is also known as Leonardo Bonacci, Leonardo of Pisa, Leonardo Pisano Bigollo. Fibonacci popularized the Hindu–Arabic numeral system in the Western World primarily through his composition in 1202 of Liber Abaci and he also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci. Fibonacci was born around 1175 to Guglielmo Bonacci, a wealthy Italian merchant and, by some accounts, Guglielmo directed a trading post in Bugia, a port in the Almohad dynastys sultanate in North Africa. Fibonacci travelled with him as a boy, and it was in Bugia that he learned about the Hindu–Arabic numeral system. Fibonacci travelled extensively around the Mediterranean coast, meeting with many merchants and he soon realised the many advantages of the Hindu-Arabic system. In 1202, he completed the Liber Abaci which popularized Hindu–Arabic numerals in Europe, Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. The date of Fibonaccis death is not known, but it has estimated to be between 1240 and 1250, most likely in Pisa. In the Liber Abaci, Fibonacci introduced the so-called modus Indorum, the book advocated numeration with the digits 0–9 and place value. The book was well-received throughout educated Europe and had a impact on European thought. No copies of the 1202 edition are known to exist, the book also discusses irrational numbers and prime numbers. Liber Abaci posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions, the solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonaccis Liber Abaci contains the earliest known description of the sequence outside of India, in the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0,1,1,2, as modern mathematicians do but with 1,1,2, etc. He carried the calculation up to the place, that is 233. Fibonacci did not speak about the ratio as the limit of the ratio of consecutive numbers in this sequence. In the 19th century, a statue of Fibonacci was constructed and raised in Pisa, today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli. There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers, examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period
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Tycho Brahe
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Tycho Brahe, born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations. He was born in the then Danish peninsula of Scania, well known in his lifetime as an astronomer, astrologer and alchemist, he has been described as the first competent mind in modern astronomy to feel ardently the passion for exact empirical facts. His observations were some five times more accurate than the best available observations at the time, an heir to several of Denmarks principal noble families, he received a comprehensive education. He took an interest in astronomy and in the creation of more instruments of measurement. His system correctly saw the Moon as orbiting Earth, and the planets as orbiting the Sun, furthermore, he was the last of the major naked eye astronomers, working without telescopes for his observations. In his De nova stella of 1573, he refuted the Aristotelian belief in a celestial realm. Using similar measurements he showed that comets were also not atmospheric phenomena, as previously thought, on the island he founded manufactories, such as a paper mill, to provide material for printing his results. He built an observatory at Benátky nad Jizerou, there, from 1600 until his death in 1601, he was assisted by Johannes Kepler, who later used Tychos astronomical data to develop his three laws of planetary motion. Tychos body has been exhumed twice, in 1901 and 2010, to examine the circumstances of his death, both of his grandfathers and all of his great grandfathers had served as members of the Danish kings Privy Council. His paternal grandfather and namesake Thyge Brahe was the lord of Tosterup Castle in Scania, Tychos father Otte Brahe, like his father a royal Privy Councilor, married Beate Bille, who was herself a powerful figure at the Danish court holding several royal land titles. Both parents are buried under the floor of Kågeröd Church, four kilometres east of Knutstorp, Tycho was born at his familys ancestral seat of Knutstorp Castle, about eight kilometres north of Svalöv in then Danish Scania. He was the oldest of 12 siblngs,8 of whom lived to adulthood and his twin brother died before being baptized. Tycho later wrote an ode in Latin to his dead twin, an epitaph, originally from Knutstorp, but now on a plaque near the church door, shows the whole family, including Tycho as a boy. When he was two years old Tycho was taken away to be raised by his uncle Jørgen Thygesen Brahe. It is unclear why the Otte Brahe reached this arrangement with his brother, Tycho later wrote that Jørgen Brahe raised me and generously provided for me during his life until my eighteenth year, he always treated me as his own son and made me his heir. From ages 6 to 12, Tycho attended Latin school, probably in Nykøbing, at age 12, on 19 April 1559, Tycho began studies at the University of Copenhagen. There, following his uncles wishes, he studied law, but also studied a variety of other subjects, at the University, Aristotle was a staple of scientific theory, and Tycho likely received a thorough training in Aristotelian physics and cosmology. He experienced the solar eclipse of 21 August 1560, and was impressed by the fact that it had been predicted
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Longomontanus
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Christen Sørensen Longomontanus was a Danish astronomer. The name Longomontanus was a Latinized form of the name of the village of Lomborg, Jutland, Denmark and his father, a laborer called Søren, or Severin, died when Christen was eight years old. An uncle took charge of the child, and had him educated at Lemvig, there he attended the grammar school, working as a labourer to pay his expenses, and in 1588 went to Copenhagen with a high reputation for learning and ability. Engaged by Tycho Brahe in 1589 as his assistant in his astronomical observatory of Uraniborg. Having left the island of Hven with his master, he obtained his discharge at Copenhagen on 1 June 1597 and he rejoined Tycho at Prague in January 1600, and having completed the Tychonic lunar theory, turned homeward again in August. Appointed in 1603 rector of the school of Viborg, he was elected two years later to a professorship in the University of Copenhagen, and his promotion to the chair of mathematics ensued in 1607 and this post was held by Longomontanus till his death in 1647. Longomontanus was not an advanced thinker and he adhered to Tychos erroneous views about refraction, believed that comets were messengers of evil, and imagined that he had squared the circle. He found that the circle diameter is 43 has for its circumference the square root of 18252 which gives 3.14185. for the value of π. John Pell and others tried in vain to convince him of his error and he inaugurated, at Copenhagen in 1632, the erection of a stately astronomical tower, but did not live to witness its completion. King Christian IV of Denmark, to whom he dedicated his Astronomia Danica, however, it was Longomontanus who really developed Tychos geoheliocentric model empirically and publicly to common acceptance in the 17th century in his 1622 astronomical tables. When Tycho died in 1601, his program for the restoration of astronomy was unfinished, Longomontanus, Tychos sole disciple, assumed the responsibility and fulfilled both tasks in his voluminous Astronomia Danica. Regarded as the testament of Tycho, the work was received in seventeenth-century astronomical literature. But unlike Tychos, his geoheliocentric model gave the Earth a daily rotation as in the models of Ursus and Roslin, as an indication of his books popularity and of the semi-Tychonic system, it was reprinted in 1640 and 1663. Some historians of science claim Kepler’s 1627 Rudolphine Tables based on Tycho Brahe’s observations were more accurate than any previous tables, but nobody has ever demonstrated they were more accurate than Longomontanus’s 1622 Danish Astronomy tables, also based upon Tycho’s observations. His major works in mathematics and astronomy were, Systematis Mathematici, cyclometria e Lunulis reciproce demonstrata, etc. Disputatio de Eclipsibus Astronomia Danica, etc, Disputationes quatuor Astrologicae Pentas Problematum Philosophiae De Chronolabio Historico, seu de Tempore Disputationes tres Geometriae quaesita XIII. Admiranda Operatio trium Numerorum 6,7,8, etc, caput tertium Libri primi de absoluta Mensura Rotundi plani, etc. The lunar crater Longomontanus was named after him and it is located near the Tycho crater
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Paul Wittich
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Wittich was born in Breslau, Silesia, and studied at the universities of Leipzig, Wittenberg and Frankfurt/Oder. About 1580 Wittich stayed with Tycho Brahe on his island Hven in Öresund and he then was employed by Landgraf Wilhelm IV. of Hessen-Kassel. Wittich may have influenced by Valentin Naboths book Primarum de coelo et terra in adopting the Capellan system to explain the motion of the inferior planets. Thus the question of whether the daily parallax of Mars was ever greater than that of the Sun was crucial to whether Wittichs model was observationally tenable or not and it seems its credibility rested solely upon his aristocratic social status rather than any scientific evidence. The latter differed from Tychos only in respect of its non-intersecting Martian, consequently this left only the Copernican and Wittichan Capellan models compatible with both solid orbs and the phases of Venus. Thus by 1610 it seems the only observationally tenable candidate for a model with solid celestial orbs was Wittichs Capellan system. Indeed even Newtons arguments for this stated in his commentary on Phenomenon 3 of Book 3 of his Principia were notably invalid
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Trigonometric identities
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Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles and these identities are useful whenever expressions involving trigonometric functions need to be simplified. This article uses Greek letters such as alpha, beta, gamma, several different units of angle measure are widely used, including degrees, radians, and gradians,1 full circle =360 degrees = 2π radians =400 gons. The following table shows the conversions and values for some common angles, all angles in this article are re-assumed to be in radians, but angles ending in a degree symbol are in degrees. Per Nivens theorem multiples of 30° are the angles that are a rational multiple of one degree and also have a rational sine or cosine. The secondary trigonometric functions are the sine and cosine of an angle and these are sometimes abbreviated sin and cos, respectively, where θ is the angle, but the parentheses around the angle are often omitted, e. g. sin θ and cos θ. The sine of an angle is defined in the context of a right triangle, the tangent of an angle is the ratio of the sine to the cosine, tan θ = sin θ cos θ. These definitions are sometimes referred to as ratio identities, the inverse trigonometric functions are partial inverse functions for the trigonometric functions. For example, the function for the sine, known as the inverse sine or arcsine, satisfies sin = x for | x | ≤1. This can be viewed as a version of the Pythagorean theorem, and follows from the equation x2 + y2 =1 for the unit circle. Dividing this identity by either cos2 θ or sin2 θ yields the other two Pythagorean identities,1 + tan 2 θ = sec 2 θ and 1 + cot 2 θ = csc 2 θ. For example, the formula was used to calculate the distance between two points on a sphere. By examining the unit circle, the properties of the trigonometric functions can be established. When the trigonometric functions are reflected from certain angles, the result is one of the other trigonometric functions. This leads to the identities, Note that the sign in front of the trig function does not necessarily indicate the sign of the value. For example, +cos θ does not always mean that cos θ is positive, in particular, if θ = π, then +cos θ = −1. By shifting the function round by certain angles, it is possible to find different trigonometric functions that express particular results more simply. Some examples of this are shown by shifting functions round by π/2, π, because the periods of these functions are either π or 2π, there are cases where the new function is exactly the same as the old function without the shift
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Sine function
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In mathematics, the sine is a trigonometric function of an angle. More generally, the definition of sine can be extended to any value in terms of the length of a certain line segment in a unit circle. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy, via translation from Sanskrit to Arabic and then from Arabic to Latin. The word sine comes from a Latin mistranslation of the Arabic jiba, to define the trigonometric functions for an acute angle α, start with any right triangle that contains an angle of measure α, in the accompanying figure, angle A in triangle ABC has measure α. The three sides of the triangle are named as follows, The opposite side is the side opposite to the angle of interest, the hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle, the adjacent side is the remaining side, in this case side b. It forms a side of both the angle of interest and the right angle, once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse. As stated, the value sin appears to depend on the choice of right triangle containing an angle of measure α, however, this is not the case, all such triangles are similar, and so the ratio is the same for each of them. The trigonometric functions can be defined in terms of the rise, run, when the length of the line segment is 1, sine takes an angle and tells the rise. Sine takes an angle and tells the rise per unit length of the line segment, rise is equal to sin θ multiplied by the length of the line segment. In contrast, cosine is used for telling the run from the angle, arctan is used for telling the angle from the slope. The line segment is the equivalent of the hypotenuse in the right-triangle, in trigonometry, a unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos θ and sin, the points distance from the origin is always 1. Unlike the definitions with the triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can also be achieved by requiring certain symmetries and that sine be a periodic function. Exact identities, These apply for all values of θ. sin = cos =1 csc The reciprocal of sine is cosecant, i. e. the reciprocal of sin is csc, or cosec. Cosecant gives the ratio of the length of the hypotenuse to the length of the opposite side, the inverse function of sine is arcsine or inverse sine
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Book of Revelation
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Its title is derived from the first word of the text, written in Koine Greek, apokalypsis, meaning unveiling or revelation. The Book of Revelation is the apocalyptic document in the New Testament canon. The author names himself in the text as John, but his identity remains a point of academic debate. Modern scholarship generally takes a different view, and many consider that nothing can be known about the author except that he was a Christian prophet, Some modern scholars characterise Revelations author as a putative figure whom they call John of Patmos. The bulk of traditional sources date the book to the reign of the emperor Domitian, the book spans three literary genres, the epistolary, the apocalyptic, and the prophetic. It begins with John, on the island of Patmos in the Aegean and he then describes a series of prophetic visions, including figures such as the Whore of Babylon and the Beast, culminating in the Second Coming of Jesus. The title is taken from the first word of the book in Koine Greek, ἀποκάλυψις apokalypsis, the author names himself as John, but it is currently considered unlikely that the author of Revelation was also the author of the Gospel of John. All that is known is that this John was a Jewish Christian prophet, probably belonging to a group of such prophets and his precise identity remains unknown, and modern scholarship commonly refers to him as John of Patmos. 70 AD is the date of writing according to Martha Himmelfarb in the recently published Blackwell series. Revelation is an apocalyptic prophecy with an epistolary introduction addressed to seven churches in the Roman province of Asia, Apocalypse means the revealing of divine mysteries, John is to write down what is revealed and send it to the seven churches. The entire book constitutes the letter—the letters to the seven churches are introductions to the rest of the book. While the dominant genre is apocalyptic, the author himself as a Christian prophet, Revelation uses the word in various forms twenty-one times. The predominant view is that Revelation alludes to the Old Testament although it is difficult among scholars to agree on the number of allusions or the allusions themselves. Revelation rarely quotes directly from the Old Testament, almost every verse alludes to or echoes older scriptures. Over half of the stem from Daniel, Ezekiel, Psalms. He very frequently combines multiple references, and again the style makes it impossible to be certain to what extent he did so consciously. Revelation was the last book accepted into the Christian biblical canon and it was considered tainted because the heretical sect of the Montanists relied on it and doubts were raised over its Jewishness and authorship. Dionysius, bishop of Alexandria, disciple of Origen wrote that the Book of Revelation could have been written by Cerinthus although he himself did not adopt the view that Cerinthus was the writer and he regarded the Apocalypse as the work of an inspired man but not of an Apostle
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Chronography
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Chronology is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events and it is also the determination of the actual temporal sequence of past events. It is also part of the discipline of history, including history, the earth sciences. Chronology is the science of locating historical events in time and it relies upon chronometry, which is also known as timekeeping, and historiography, which examines the writing of history and the use of historical methods. Radiocarbon dating estimates the age of living things by measuring the proportion of carbon-14 isotope in their carbon content. Dendrochronology is used in turn as a reference for radiocarbon dating curves. The familiar terms calendar and era concern two complementary concepts of chronology. Dionysius Exiguus was the founder of that era, which is nowadays the most widespread dating system on earth, an epoch is the date when an era begins. Ab Urbe condita is Latin for from the founding of the City and it was used to identify the Roman year by a few Roman historians. Modern historians use it more frequently than the Romans themselves did. Before the advent of the critical edition of historical Roman works, AUC was indiscriminately added to them by earlier editors. It was used systematically for the first time only about the year 400, pope Boniface IV, in about the year 600, seems to have been the first who made a connection between these this era and Anno Domini. Dionysius Exiguus’ Anno Domini era was extended by Bede to the complete Christian era, while of critical importance to the historian, methods of determining chronology are used in most disciplines of science, especially astronomy, geology, paleontology and archaeology. In the absence of written history, with its chronicles and king lists and this method of dating is known as seriation. Known wares discovered at strata in sometimes quite distant sites, the product of trade, laboratory techniques developed particularly after mid-20th century helped constantly revise and refine the chronologies developed for specific cultural areas. Unrelated dating methods help reinforce a chronology, an axiom of corroborative evidence, ideally, archaeological materials used for dating a site should complement each other and provide a means of cross-checking. Conclusions drawn from just one unsupported technique are usually regarded as unreliable, the fundamental problem of chronology is to synchronize events. By synchronizing an event it becomes possible to relate it to the current time, among historians, a typical need to is to synchronize the reigns of kings and leaders in order to relate the history of one country or region to that of another