1.
1830 in science
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The year 1830 in science and technology involved some significant events, listed below. March 16 – Great Comet of 1830 first observed in Mauritius, johann Heinrich Mädler and Wilhelm Beer produce the first map of the surface of Mars. Charles Bell publishes his Nervous System of the Human Body, william Jackson Hooker commences publication of The British Flora. October 14 – HMS Beagle returns to England from her first voyage, Charles Lyell publishes the first volume of his Principles of Geology, being an attempt to explain the former changes of the Earths surface, by reference to causes now in operation. Thomas Southwood Smith publishes the standard textbook A Treatise on Fever in London, july 13 – John Ruggles is granted United States patent No. 1, for applying rack railway equipment to the Locomotive steam-engine for rail, august 31 – Edwin Budding is granted a United Kingdom patent for the lawnmower. Aeneas Coffey is granted a United Kingdom patent for a column still. Charles Babbage publishes Reflections on the Decline of Science in England, copley Medal, not awarded March 5 – Étienne-Jules Marey, physiologist. March 5 – Charles Wyville Thompson, marine biologist, april 21 – Clémence Royer, French anthropologist. May 10 – François-Marie Raoult, chemist, august 19 – Lothar Meyer, chemist. October 24 – Marianne North, botanist, november 20 – Sigismond Jaccoud, physician. March 2 – Samuel Thomas von Sömmerring, physician, anatomist, paleontologist, March 29 – James Rennell, cartographer and oceanographer. May 16 – Joseph Fourier, mathematician
2.
1843 in science
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The year 1843 in science and technology involved some significant events, listed below. March 11–14 – Eta Carinae flares to become the second brightest star, february 5–April 19 – Great March Comet observed. Heinrich Schwabe reports a periodic change in the number of sunspots, they wax, carl Mosander discovers Terbium and Erbium. John J. Waterston produces an account of the theory of gases. October 16 – William Rowan Hamilton discovers the calculus of quaternions, arthur Cayley and James Joseph Sylvester found the algebraic invariant theory. John T. Graves discovers the octonions, pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem. James Prescott Joule experimentally finds the mechanical equivalent of heat, british surgeon James Braid publishes Neurypnology, or the Rationale of Nervous Sleep, a key text in the history of hypnotism. Oliver Wendell Holmes, Sr. argues that puerperal fever is spread by lack of hygiene in physicians, March 25 – Completion of the Thames Tunnel, the first bored underwater tunnel in the world. July 19 – Launch of SS Great Britain, the first iron-hulled, november 21 – Thomas Hancock patents the vulcanisation of rubber using sulphur in the United Kingdom The steam powered rotary printing press is invented by Richard March Hoe in the United States. Robert Stirling and his brother James convert a steam engine at a Dundee factory to operate as a Stirling engine, the first public telegraph line in the United Kingdom is laid between Paddington and Slough. Copley Medal, Jean-Baptiste Dumas Wollaston Medal for Geology, Jean-Baptiste Elie de Beaumont, Pierre Armand Dufrenoy January 13 – David Ferrier, may 6 – G. K. Gilbert, American geologist. June 12 – David Gill, Scottish astronomer, june 23 – Paul Heinrich von Groth, German mineralogist. July 24 – William de Wiveleslie Abney, English astronomer, august 17 – Alexandre Lacassagne, French forensic scientist. November 30 – Martha Ripley, American physician, july 25 – Charles Macintosh, Scottish inventor of a waterproof fabric. August 10 – Robert Adrain, Irish American mathematician, september 11 – Joseph Nicollet, French geographer, explorer, mathematician and astronomer. September 19 – Gaspard-Gustave Coriolis, French mathematician and discoverer of the Coriolis effect, september 30 – Richard Harlan, American zoologist. November 16 – Abraham Colles, Anglo-Irish surgeon
3.
1846 in science
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The year 1846 in science and technology involved some significant events, listed below. February 20 – Francesco de Vico discovers comet 122P/de Vico, june 1 – Urbain Le Verrier predicts the existence and location of Neptune from irregularities in the orbit of Uranus. August 8 – Neptune observed but not recognised by James Challis, august 31 – Urbain Le Verrier publishes full details of the predicted orbit and the mass of the new planet. September 23 – Johann Galle discovers Neptune, october 10 – William Lassell discovers Triton, Neptunes largest moon. Royal Botanic Gardens, Melbourne, established in Australia, abraham Pineo Gesner develops a process to refine a liquid fuel, which he calls kerosene, from coal, bitumen or oil shale. December 21 – British surgeon Robert Liston carries out the first operation under anesthesia in Europe, dr J. Collis Browne formulates his laudanum-based pain-relieving Chlorodyne compound while serving in the British Indian Army. January 13 – Opening of the Milan–Venice railways 3.2 km bridge over the Venetian Lagoon between Mestre and Venice in Italy, the worlds longest since 1151, june 28 – Adolphe Sax patents the saxophone. September 10 – Elias Howe is awarded the first United States patent for a machine using a lockstitch design. Scottish-born engineer Robert William Thomson is granted his first patent for a pneumatic tyre, William Armstrongs first hydraulic crane is erected at Newcastle upon Tyne in England. Squire Whipple introduces the trapezoidal Whipple truss for bridges in the United States, copley Medal, Urbain Le Verrier Wollaston Medal, William Lonsdale September 16 – Anna Kingsford, English physician, anti-vivisectionist and vegetarian. December 12 – Eugen Baumann, German chemist, january 30 – Joseph Carpue English surgeon. March 17 – Friedrich Bessel, German mathematician, october 2 – Benjamin Waterhouse, American physician. John Bostock, English physician and geologist
4.
1837 in art
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Events from the year 1837 in art. January 20 – Death of the neo-classical architect Sir John Soane gives effect to the creation of his London house as Sir John Soanes Museum, june 1 – The Government-funded Normal School of Design, predecessor of the Royal College of Art, begins classes at Somerset House in London. July – Edward Lear leaves Knowsley Hall in England to travel to Rome, marie Louise Élisabeth Vigée-Lebrun publishes the second volume of her memoirs
5.
1837 in archaeology
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See also, other events of 1837. Antikensammlung Berlin acquires the 5th century BC red-figure pottery Berlin Foundry Cup from Volci, richard William Howard Vyse investigates the interiors of the Pyramids of Giza using blasting techniques. John Gardner Wilkinson - Manners and Customs of the Ancient Egyptians, theodore M. Davis, American Egyptological excavation sponsor
6.
1837 in architecture
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The year 1837 in architecture involved some significant events. June 10 - Galerie des Batailles at the Palace of Versailles in France, july 13 - Christ Church, St Pancras, London, designed by James Pennethorne, is consecrated. July 20 - Euston railway station, the first main line station in London, is opened, great Stove or Conservatory at Chatsworth House in England, designed by Joseph Paxton, is begun, it is the largest glass building in the world at this time. Major reconstruction of Penrhyn Castle in North Wales by Thomas Hopper is largely completed, Rock Park, Rock Ferry, England, laid out by Jonathan Bennison. Grand Prix de Rome, architecture, Jean-Baptiste Guenepin, January 11 - The Royal Institute of British Architects in London is granted its royal charter. January 20 - Death of English neo-classical architect Sir John Soane gives effect to the creation of his London house as Sir John Soanes Museum,28 May - George Ashlin, Irish architect 4 June - Jean-Louis Pascal, French architect 15 December - George B. Post, American architect January 20 - Sir John Soane, English architect
7.
Science
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Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The formal sciences are often excluded as they do not depend on empirical observations, disciplines which use science, like engineering and medicine, may also be considered to be applied sciences. However, during the Islamic Golden Age foundations for the method were laid by Ibn al-Haytham in his Book of Optics. In the 17th and 18th centuries, scientists increasingly sought to formulate knowledge in terms of physical laws, over the course of the 19th century, the word science became increasingly associated with the scientific method itself as a disciplined way to study the natural world. It was during this time that scientific disciplines such as biology, chemistry, Science in a broad sense existed before the modern era and in many historical civilizations. Modern science is distinct in its approach and successful in its results, Science in its original sense was a word for a type of knowledge rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other, for example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of calendars, techniques for making poisonous plants edible. For this reason, it is claimed these men were the first philosophers in the strict sense and they were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by scientists as a more appropriate interest for lower class artisans. A clear-cut distinction between formal and empirical science was made by the pre-Socratic philosopher Parmenides, although his work Peri Physeos is a poem, it may be viewed as an epistemological essay on method in natural science. Parmenides ἐὸν may refer to a system or calculus which can describe nature more precisely than natural languages. Physis may be identical to ἐὸν and he criticized the older type of study of physics as too purely speculative and lacking in self-criticism. He was particularly concerned that some of the early physicists treated nature as if it could be assumed that it had no intelligent order, explaining things merely in terms of motion and matter. The study of things had been the realm of mythology and tradition, however. Aristotle later created a less controversial systematic programme of Socratic philosophy which was teleological and he rejected many of the conclusions of earlier scientists. For example, in his physics, the sun goes around the earth, each thing has a formal cause and final cause and a role in the rational cosmic order. Motion and change is described as the actualization of potentials already in things, while the Socratics insisted that philosophy should be used to consider the practical question of the best way to live for a human being, they did not argue for any other types of applied science
8.
Technology
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Technology is the collection of techniques, skills, methods and processes used in the production of goods or services or in the accomplishment of objectives, such as scientific investigation. Technology can be the knowledge of techniques, processes, and the like, the human species use of technology began with the conversion of natural resources into simple tools. The steady progress of technology has brought weapons of ever-increasing destructive power. It has helped develop more advanced economies and has allowed the rise of a leisure class, many technological processes produce unwanted by-products known as pollution and deplete natural resources to the detriment of Earths environment. Various implementations of technology influence the values of a society and raise new questions of the ethics of technology, examples include the rise of the notion of efficiency in terms of human productivity, and the challenges of bioethics. Philosophical debates have arisen over the use of technology, with disagreements over whether technology improves the condition or worsens it. The use of the technology has changed significantly over the last 200 years. Before the 20th century, the term was uncommon in English, the term was often connected to technical education, as in the Massachusetts Institute of Technology. The term technology rose to prominence in the 20th century in connection with the Second Industrial Revolution, the terms meanings changed in the early 20th century when American social scientists, beginning with Thorstein Veblen, translated ideas from the German concept of Technik into technology. In German and other European languages, a distinction exists between technik and technologie that is absent in English, which translates both terms as technology. By the 1930s, technology referred not only to the study of the industrial arts, dictionaries and scholars have offered a variety of definitions. Ursula Franklin, in her 1989 Real World of Technology lecture, gave another definition of the concept, it is practice, the way we do things around here. The term is used to imply a specific field of technology, or to refer to high technology or just consumer electronics. Bernard Stiegler, in Technics and Time,1, defines technology in two ways, as the pursuit of life by other than life, and as organized inorganic matter. Technology can be most broadly defined as the entities, both material and immaterial, created by the application of mental and physical effort in order to some value. In this usage, technology refers to tools and machines that may be used to solve real-world problems and it is a far-reaching term that may include simple tools, such as a crowbar or wooden spoon, or more complex machines, such as a space station or particle accelerator. Tools and machines need not be material, virtual technology, such as software and business methods. W. Brian Arthur defines technology in a broad way as a means to fulfill a human purpose
9.
Charles Darwin
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Charles Robert Darwin, FRS FRGS FLS FZS was an English naturalist, geologist and biologist, best known for his contributions to the science of evolution. Darwin published his theory of evolution with compelling evidence in his 1859 book On the Origin of Species, by the 1870s, the scientific community and much of the general public had accepted evolution as a fact. In modified form, Darwins scientific discovery is the theory of the life sciences. Darwins early interest in nature led him to neglect his education at the University of Edinburgh, instead. Studies at the University of Cambridge encouraged his passion for natural science, puzzled by the geographical distribution of wildlife and fossils he collected on the voyage, Darwin began detailed investigations and in 1838 conceived his theory of natural selection. Although he discussed his ideas with several naturalists, he needed time for extensive research and he was writing up his theory in 1858 when Alfred Russel Wallace sent him an essay that described the same idea, prompting immediate joint publication of both of their theories. Darwins work established evolutionary descent with modification as the dominant scientific explanation of diversification in nature, in 1871 he examined human evolution and sexual selection in The Descent of Man, and Selection in Relation to Sex, followed by The Expression of the Emotions in Man and Animals. His research on plants was published in a series of books, Darwin has been described as one of the most influential figures in human history, and he was honoured by burial in Westminster Abbey. Charles Robert Darwin was born in Shrewsbury, Shropshire, on 12 February 1809, at his familys home and he was the fifth of six children of wealthy society doctor and financier Robert Darwin and Susannah Darwin. He was the grandson of two prominent abolitionists, Erasmus Darwin on his fathers side, and Josiah Wedgwood on his mothers side, both families were largely Unitarian, though the Wedgwoods were adopting Anglicanism. The eight-year-old Charles already had a taste for history and collecting when he joined the day school run by its preacher in 1817. From September 1818, he joined his older brother Erasmus attending the nearby Anglican Shrewsbury School as a boarder and he found lectures dull and surgery distressing, so neglected his studies. He learned taxidermy in around 40 daily hour-long sessions from John Edmonstone, one day, Grant praised Lamarcks evolutionary ideas. Darwin was astonished by Grants audacity, but had recently read similar ideas in his grandfather Erasmus journals, Darwin was rather bored by Robert Jamesons natural-history course, which covered geology - including the debate between Neptunism and Plutonism. He learned the classification of plants, and assisted with work on the collections of the University Museum, as Darwin was unqualified for the Tripos, he joined the ordinary degree course in January 1828. He preferred riding and shooting to studying, when his own exams drew near, Darwin focused on his studies and was delighted by the language and logic of William Paleys Evidences of Christianity. In his final examination in January 1831 Darwin did well, coming out of 178 candidates for the ordinary degree. Darwin had to stay at Cambridge until June 1831, inspired with a burning zeal to contribute, Darwin planned to visit Tenerife with some classmates after graduation to study natural history in the tropics
10.
Transmutation of species
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The debate over them was an important stage in the history of evolutionary thought and would influence the subsequent reaction to Darwins theory. Transmutation was one of the commonly used for evolutionary ideas in the 19th century before Charles Darwin published On The Origin of Species. Transmutation had previously used as a term in alchemy to describe the transformation of base metals into gold. Transformation is another word used quite as often as transmutation in this context and these early 19th century evolutionary ideas played an important role in the history of evolutionary thought. The terminology did not settle down until some time after the publication of the Origin of Species. The word evolution was quite a late-comer, it can be seen in Herbert Spencers Social Statics of 1851, and there is at least one earlier example, jean-Baptiste Lamarck proposed a hypothesis on the transmutation of species in Philosophie Zoologique. Lamarck did not believe that all living things shared a common ancestor, rather he believed that simple forms of life were created continuously by spontaneous generation. Lamarck also recognized that species were adapted to their environment and he argued that these changes would be inherited by the next generation and produce slow adaptation to the environment. Grant developed Lamarcks and Erasmus Darwins ideas of transmutation and evolutionism, as a young student Charles Darwin joined Grant in investigations of the life cycle of marine animals. Jamesons course closed with lectures on the Origin of the Species of Animals, in 1844 the Scottish publisher Robert Chambers anonymously published an influential and extremely controversial book of popular science entitled Vestiges of the Natural History of Creation. This book proposed a scenario for the origins of the solar system. It claimed that the record showed a progressive ascent of animals with current animals being branches off a main line that leads progressively to humanity. It implied that the lead to the unfolding of a preordained plan that had been woven into the laws that governed the universe. Darwin himself openly deplored the authors poverty of intellect, and dismissed it as a literary curiosity and it also influenced some younger naturalists, including Alfred Russel Wallace, to take an interest in the idea of transmutation. Ideas about the transmutation of species were associated with the radical materialism of the enlightenment and were greeted with hostility by more conservative thinkers. Cuvier attacked the ideas of Lamarck and Geoffroy Saint-Hilaire, agreeing with Aristotle that species were immutable and he also noted that drawings of animals and animal mummies from Egypt, which were thousands of years old, showed no signs of change when compared with modern animals. The strength of Cuviers arguments and his reputation as a leading scientist helped keep transmutational ideas out of the mainstream for decades. Instead, he advocated a form of creation, in which each species had its centre of creation and was designed for this particular habitat
11.
Public Garden (Boston)
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The Public Garden, also known as Boston Public Garden, is a large park in the heart of Boston, Massachusetts, adjacent to Boston Common. Bostons Back Bay, including the land the garden sits on, was mudflats until filling began in the early 1800s, the land of the Public Garden was the earliest filled, as the area that is now Charles Street had been used as a ropewalk since 1796. The town of Boston granted ropemakers use of the land on July 30,1794, as a condition of its use, the ropewalks proprietors were required to build a seawall and fill in the land which is now Charles Street and the land immediately bordering it. Much of the material came from Mount Vernon, formerly a hill in the Beacon Hill area of Boston. Initially, gravel and dirt were brought from the hill to the area by handcart. In February 1824, the city of Boston purchased back the granted to the ropemakers. The next year, a proposal to turn the land into a graveyard was defeated by a vote of 1632 to 176, the Public Garden was established in 1837, when philanthropist Horace Gray petitioned for the use of land as the first public botanical garden in the United States. By 1839, a corporation was formed, called Horace Gray and Associates, the corporation was chartered with creating what is now the Boston Public Garden. Nonetheless, there was constant pressure for the land to be sold to private interests for the construction of new housing, while most of the land of the present-day garden had been filled in by the mid-1800s, the area of the Back Bay remained an undeveloped tidal basin. The City of Boston petitioned the state to grant control over the basin, in hopes of generating significant revenue from any developments that would be built after filling it in. In the agreement, Boston gave up its rights to build upon the Public Garden, in return, it received a strip of land which is now a part of the garden, abutting Arlington Street. In October 1859, Alderman Crane submitted the plan for the Garden to the Committee on the Common and Public Squares. Construction began quickly on the property, with the pond being finished that year, today the north side of the pond has a small island, but it originally was a peninsula, connected to the land. The site became so popular with lovers that John Galvin, the city forester, the 24 acres landscape was designed by George F. Meacham. The paths and flower beds were laid out by the city engineer, James Slade, the plan for the garden included a number of fountains and statues, many of which were erected in the late 1860s. The most notable statue is perhaps that of George Washington, done in 1869 by Thomas Ball, the signature suspension bridge over the middle of the pond was erected in 1869. Gas lamps were used to light the garden at night. A flagpole stands today on the side of the garden, close to Charles Street
12.
Boston
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Boston is the capital and most populous city of the Commonwealth of Massachusetts in the United States. Boston is also the seat of Suffolk County, although the county government was disbanded on July 1,1999. The city proper covers 48 square miles with a population of 667,137 in 2015, making it the largest city in New England. Alternately, as a Combined Statistical Area, this wider commuting region is home to some 8.1 million people, One of the oldest cities in the United States, Boston was founded on the Shawmut Peninsula in 1630 by Puritan settlers from England. It was the scene of several key events of the American Revolution, such as the Boston Massacre, the Boston Tea Party, the Battle of Bunker Hill, and the Siege of Boston. Upon U. S. independence from Great Britain, it continued to be an important port and manufacturing hub as well as a center for education, through land reclamation and municipal annexation, Boston has expanded beyond the original peninsula. Its rich history attracts many tourists, with Faneuil Hall alone drawing over 20 million visitors per year, Bostons many firsts include the United States first public school, Boston Latin School, first subway system, the Tremont Street Subway, and first public park, Boston Common. Bostons economic base also includes finance, professional and business services, biotechnology, information technology, the city has one of the highest costs of living in the United States as it has undergone gentrification, though it remains high on world livability rankings. Bostons early European settlers had first called the area Trimountaine but later renamed it Boston after Boston, Lincolnshire, England, the renaming on September 7,1630 was by Puritan colonists from England who had moved over from Charlestown earlier that year in quest of fresh water. Their settlement was limited to the Shawmut Peninsula, at that time surrounded by the Massachusetts Bay and Charles River. The peninsula is thought to have been inhabited as early as 5000 BC, in 1629, the Massachusetts Bay Colonys first governor John Winthrop led the signing of the Cambridge Agreement, a key founding document of the city. Puritan ethics and their focus on education influenced its early history, over the next 130 years, the city participated in four French and Indian Wars, until the British defeated the French and their Indian allies in North America. Boston was the largest town in British America until Philadelphia grew larger in the mid-18th century, Bostons harbor activity was significantly curtailed by the Embargo Act of 1807 and the War of 1812. Foreign trade returned after these hostilities, but Bostons merchants had found alternatives for their investments in the interim. Manufacturing became an important component of the economy, and the citys industrial manufacturing overtook international trade in economic importance by the mid-19th century. Boston remained one of the nations largest manufacturing centers until the early 20th century, a network of small rivers bordering the city and connecting it to the surrounding region facilitated shipment of goods and led to a proliferation of mills and factories. Later, a network of railroads furthered the regions industry. Boston was a port of the Atlantic triangular slave trade in the New England colonies
13.
Botanical garden
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A botanical garden or botanic garden is a garden dedicated to the collection, cultivation and display of a wide range of plants labelled with their botanical names. Visitor services at a botanical garden might include tours, educational displays, art exhibitions, book rooms, open-air theatrical and musical performances, over the years, botanical gardens, as cultural and scientific organisations, have responded to the interests of botany and horticulture. The role of major botanical gardens worldwide has been considered so similar as to fall within textbook definitions. The following definition was produced by staff of the Liberty Hyde Bailey Hortorium of Cornell University in 1976, each botanical garden naturally develops its own special fields of interests depending on its personnel, location, extent, available funds, and the terms of its charter. It may include greenhouses, test grounds, an herbarium, an arboretum and it maintains a scientific as well as a plant-growing staff, and publication is one of its major modes of expression. This broad outline is then expanded, The botanic garden may be an independent institution, if a department of an educational institution, it may be related to a teaching program. In any case, it exists for scientific ends and is not to be restricted or diverted by other demands. It is not merely a landscaped or ornamental garden, although it may be artistic, the essential element is the intention of the enterprise, which is the acquisition and dissemination of botanical knowledge. Worldwide, there are now about 1800 botanical gardens and arboreta in about 150 countries of which about 550 are in Europe,200 in North America, and an increasing number in East Asia. These gardens attract about 150 million visitors a year, so it is surprising that many people gained their first exciting introduction to the wonders of the plant world in a botanical garden. Historically, botanical gardens exchanged plants through the publication of seed lists and this was a means of transferring both plants and information between botanical gardens. This system continues today, although the possibility of genetic piracy, the International Association of Botanic Gardens was formed in 1954 as a worldwide organisation affiliated to the International Union of Biological Sciences. In the United States, there is the American Public Gardens Association, the history of botanical gardens is closely linked to the history of botany itself. Then, in the 19th and 20th centuries, the trend was towards a combination of specialist, the idea of scientific gardens used specifically for the study of plants dates back to antiquity. In about 2800 BCE, the Chinese Emperor Shen Nung sent collectors to distant regions searching for plants with economic or medicinal value. Early medieval gardens in Islamic Spain resembled botanic gardens of the future and this was later taken over by garden chronicler Ibn Bassal until the Christian conquest in 1085 CE. Ibn Bassal then founded a garden in Seville, most of its plants being collected on an expedition that included Morocco, Persia, Sicily. The medical school of Montpelier was also founded by Spanish Arab physicians, and by 1250 CE, it included a physic garden, but the site was not given botanic garden status until 1593
14.
United States
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Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography, climate and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power. The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations. In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci
15.
Peter Gustav Lejeune Dirichlet
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His father Johann Arnold Lejeune Dirichlet was the postmaster, merchant, and city councilor. His paternal grandfather had come to Düren from Richelette, a small community 5 km north east of Liège in Belgium, although his family was not wealthy and he was the youngest of seven children, his parents supported his education. They enrolled him in a school and then private school in hope that he would later become a merchant. The young Dirichlet, who showed a strong interest in mathematics before age 12, in 1817 they sent him to the Gymnasium Bonn under the care of Peter Joseph Elvenich, a student his family knew. In 1820 Dirichlet moved to the Jesuit Gymnasium in Cologne, where his lessons with Georg Ohm helped widen his knowledge in mathematics and he left the gymnasium a year later with only a certificate, as his inability to speak fluent Latin prevented him from earning the Abitur. Dirichlet again convinced his parents to further financial support for his studies in mathematics. In 1823 he was recommended to General Foy, who hired him as a tutor to teach his children German. In June 1825 he was accepted to lecture on his partial proof for the case n=5 at the French Academy of Sciences, an exceptional feat for a 20-year-old student with no degree. His lecture at the Academy had also put Dirichlet in close contact with Fourier and Poisson, as General Foy died in November 1825 and he could not find any paying position in France, Dirichlet had to return to Prussia. Fourier and Poisson introduced him to Alexander von Humboldt, who had called to join the court of King Friedrich Wilhelm III. Humboldt also secured a letter from Gauss, who upon reading his memoir on Fermats theorem wrote with an unusual amount of praise that Dirichlet showed excellent talent. With the support of Humboldt and Gauss, Dirichlet was offered a position at the University of Breslau. However, as he had not passed a doctoral dissertation, he submitted his memoir on the Fermat theorem as a thesis to the University of Bonn, also, the Minister of Education granted him a dispensation for the Latin disputation required for the Habilitation. Dirichlet earned the Habilitation and lectured in the 1827/28 year as a Privatdozent at Breslau, while in Breslau, Dirichlet continued his number theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gausss research. Alexander von Humboldt took advantage of new results, which had also drawn enthusiastic praise from Friedrich Bessel. Given Dirichlets young age, Humboldt was only able to get him a position at the Prussian Military Academy in Berlin while remaining nominally employed by the University of Breslau. The probation was extended for three years until the position becoming definitive in 1831, after moving to Berlin, Humboldt introduced Dirichlet to the great salons held by the banker Abraham Mendelssohn Bartholdy and his family. Their house was a gathering point for Berlin artists and scientists, including Abrahams children Felix and Fanny Mendelssohn
16.
Mathematical analysis
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Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are studied in the context of real and complex numbers. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis, analysis may be distinguished from geometry, however, it can be applied to any space of mathematical objects that has a definition of nearness or specific distances between objects. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, a geometric sum is implicit in Zenos paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes The Method of Mechanical Theorems, in Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere in the 5th century, the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolles theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and his followers at the Kerala school of astronomy and mathematics further expanded his works, up to the 16th century. The modern foundations of analysis were established in 17th century Europe. During this period, calculus techniques were applied to approximate discrete problems by continuous ones, in the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the definition of continuity in 1816. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required a change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations, the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis. In the middle of the 19th century Riemann introduced his theory of integration, the last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the epsilon-delta definition of limit. Then, mathematicians started worrying that they were assuming the existence of a continuum of numbers without proof. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the size of the set of discontinuities of real functions, also, monsters began to be investigated
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Analytic number theory
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In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlets 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlets theorem on arithmetic progressions and it is well known for its results on prime numbers and additive number theory. Analytic number theory can be split up two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. Additive number theory is concerned with the structure of the integers. One of the results in additive number theory is the solution to Warings problem. Much of analytic number theory was inspired by the prime number theorem, let π be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. For example, π =4 because there are four prime numbers less than or equal to 10, adrien-Marie Legendre conjectured in 1797 or 1798 that π is approximated by the function a/, where A and B are unspecified constants. In the second edition of his book on number theory he made a more precise conjecture. But Gauss never published this conjecture, in 1838 Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li. In 1837 he published Dirichlets theorem on arithmetic progressions, using mathematical concepts to tackle an algebraic problem. In proving the theorem, he introduced the Dirichlet characters and L-functions, in 1841 he generalized his arithmetic progressions theorem from integers to the ring of Gaussian integers Z. In two papers from 1848 and 1850, the Russian mathematician Pafnuty Lvovich Chebyshev attempted to prove the law of distribution of prime numbers. In a single paper, he investigated the Riemann zeta function. He made a series of conjectures about properties of the zeta function, extending the ideas of Riemann, two proofs of the prime number theorem were obtained independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin and appeared in the same year. The biggest technical change after 1950 has been the development of sieve methods and these are combinatorial in nature, and quite varied. The extremal branch of combinatorial theory has in return been greatly influenced by the value placed in number theory on quantitative upper and lower bounds. Developments within analytic number theory are often refinements of earlier techniques, for example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane, it is now thought of in terms of finite exponential sums. The fields of approximation and transcendence theory have expanded, to the point that the techniques have been applied to the Mordell conjecture
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Series (mathematics)
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In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a sequence has defined first and last terms. To emphasize that there are a number of terms, a series is often called an infinite series. In order to make the notion of an infinite sum mathematically rigorous, given an infinite sequence, the associated series is the expression obtained by adding all those terms together, a 1 + a 2 + a 3 + ⋯. These can be written compactly as ∑ i =1 ∞ a i, by using the summation symbol ∑. The sequence can be composed of any kind of object for which addition is defined. A series is evaluated by examining the finite sums of the first n terms of a sequence, called the nth partial sum of the sequence, and taking the limit as n approaches infinity. If this limit does not exist, the infinite sum cannot be assigned a value, and, in this case, the series is said to be divergent. On the other hand, if the partial sums tend to a limit when the number of terms increases indefinitely, then the series is said to be convergent, and the limit is called the sum of the series. An example is the series from Zenos dichotomy and its mathematical representation, ∑ n =1 ∞12 n =12 +14 +18 + ⋯. The study of series is a part of mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures, in addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For any sequence of numbers, real numbers, complex numbers, functions thereof. By definition the series ∑ n =0 ∞ a n converges to a limit L if and this definition is usually written as L = ∑ n =0 ∞ a n ⇔ L = lim k → ∞ s k. When the index set is the natural numbers I = N, a series indexed on the natural numbers is an ordered formal sum and so we rewrite ∑ n ∈ N as ∑ n =0 ∞ in order to emphasize the ordering induced by the natural numbers. Thus, we obtain the common notation for a series indexed by the natural numbers ∑ n =0 ∞ a n = a 0 + a 1 + a 2 + ⋯. When the semigroup G is also a space, then the series ∑ n =0 ∞ a n converges to an element L ∈ G if. This definition is usually written as L = ∑ n =0 ∞ a n ⇔ L = lim k → ∞ s k, a series ∑an is said to converge or to be convergent when the sequence SN of partial sums has a finite limit
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Bernard Bolzano
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Bernard Bolzano was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his antimilitarist views. Bolzano wrote in German, his mother tongue, for the most part, his work came to prominence posthumously. Bolzano was the son of two pious Catholics and his father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Pragues German-speaking family Maurer. Only two of their children lived to adulthood. Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy, starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the newly created chair of philosophy of religion at Prague University in 1805. He proved to be a popular lecturer not just in religion but also in philosophy, Bolzano alienated many faculty and church leaders with his teachings of the social waste of militarism and the needlessness of war. He urged a total reform of the educational, social, upon his refusal to recant his beliefs, Bolzano was dismissed from the university in 1819. His political convictions eventually proved to be too liberal for the Austrian authorities and he was exiled to the countryside and at that point devoted his energies to his writings on social, religious, philosophical, and mathematical matters. Although forbidden to publish in journals as a condition of his exile, Bolzano continued to develop his ideas. In 1842 he moved back to Prague, where he died in 1848, Bolzano made several original contributions to mathematics. His overall philosophical stance was that, contrary to much of the mathematics of the era, it was better not to introduce intuitive ideas such as time. These works presented. a sample of a new way of developing analysis, to the foundations of mathematical analysis he contributed the introduction of a fully rigorous ε–δ definition of a mathematical limit. Bolzano was the first to recognize the greatest lower bound property of the real numbers, like several others of his day, he was skeptical of the possibility of Gottfried Leibnizs infinitesimals, that had been the earliest putative foundation for differential calculus. Bolzano also gave the first purely analytic proof of the theorem of algebra. He also gave the first purely analytic proof of the intermediate value theorem, the logical theory that Bolzano developed in this work has come to be acknowledged as ground-breaking. Other works are a four-volume Lehrbuch der Religionswissenschaft and the metaphysical work Athanasia, Bolzano also did valuable work in mathematics, which remained virtually unknown until Otto Stolz rediscovered many of his lost journal articles and republished them in 1881. Bolzano begins his work by explaining what he means by theory of science, human knowledge, he states, is made of all truths that men know or have known
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William Rowan Hamilton
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Sir William Rowan Hamilton PRIA FRSE was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and his best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the study of classical field theories such as electromagnetism. In pure mathematics, he is best known as the inventor of quaternions, Hamilton is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarked of the 18-year-old Hamilton, This young man, I do not say will be, but is, Hamilton also invented icosian calculus, which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once. Hamilton was the fourth of nine born to Sarah Hutton and Archibald Hamilton. Hamiltons father, who was from Dunboyne, worked as a solicitor, by the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim, Co. His uncle soon discovered that Hamilton had an ability to learn languages. At the age of seven he had made very considerable progress in Hebrew. These included the classical and modern European languages, and Persian, Arabic, Hindustani, Sanskrit, in September 1813 the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, an older than Hamilton. The two were pitted against each other in a mental arithmetic contest with Colburn emerging the clear victor, in reaction to his defeat, Hamilton dedicated less time to studying languages and more time to studying mathematics. Hamilton was part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, which he entered at age 18. He studied both classics and mathematics, and was appointed Professor of Astronomy in 1827, prior to his taking up residence at Dunsink Observatory where he spent the rest of his life. Hamilton made important contributions to optics and to classical mechanics and his first discovery was in an early paper that he communicated in 1823 to Dr. Brinkley, who presented it under the title of Caustics in 1824 to the Royal Irish Academy. It was referred as usual to a committee, while their report acknowledged its novelty and value, they recommended further development and simplification before publication. Between 1825 and 1828 the paper grew to an immense size, but it also became more intelligible, and the features of the new method were now easily to be seen. Until this period Hamilton himself seems not to have fully understood either the nature or importance of optics and he proposed for it when he first predicted its existence in the third supplement to his Systems of Rays, read in 1832
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Complex number
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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i2 = −1. In this expression, a is the part and b is the imaginary part of the complex number. If z = a + b i, then ℜ z = a, ℑ z = b, Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point in the complex plane, a complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the numbers are a field extension of the ordinary real numbers. As well as their use within mathematics, complex numbers have applications in many fields, including physics, chemistry, biology, economics, electrical engineering. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers and he called them fictitious during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to equations that have no solutions in real numbers. For example, the equation 2 = −9 has no real solution, Complex numbers provide a solution to this problem. The idea is to extend the real numbers with the unit i where i2 = −1. According to the theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. A complex number is a number of the form a + bi, for example, −3.5 + 2i is a complex number. The real number a is called the part of the complex number a + bi. By this convention the imaginary part does not include the unit, hence b. The real part of a number z is denoted by Re or ℜ. For example, Re = −3.5 Im =2, hence, in terms of its real and imaginary parts, a complex number z is equal to Re + Im ⋅ i. This expression is known as the Cartesian form of z. A real number a can be regarded as a number a + 0i whose imaginary part is 0
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Real number
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In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced in the 17th century by René Descartes, the real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2. Included within the irrationals are the numbers, such as π. Real numbers can be thought of as points on a long line called the number line or real line. Any real number can be determined by a possibly infinite decimal representation, such as that of 8.632, the real line can be thought of as a part of the complex plane, and complex numbers include real numbers. These descriptions of the numbers are not sufficiently rigorous by the modern standards of pure mathematics. All these definitions satisfy the definition and are thus equivalent. The statement that there is no subset of the reals with cardinality greater than ℵ0. Simple fractions were used by the Egyptians around 1000 BC, the Vedic Sulba Sutras in, c.600 BC, around 500 BC, the Greek mathematicians led by Pythagoras realized the need for irrational numbers, in particular the irrationality of the square root of 2. Arabic mathematicians merged the concepts of number and magnitude into a general idea of real numbers. In the 16th century, Simon Stevin created the basis for modern decimal notation, in the 17th century, Descartes introduced the term real to describe roots of a polynomial, distinguishing them from imaginary ones. In the 18th and 19th centuries, there was work on irrational and transcendental numbers. Johann Heinrich Lambert gave the first flawed proof that π cannot be rational, Adrien-Marie Legendre completed the proof, Évariste Galois developed techniques for determining whether a given equation could be solved by radicals, which gave rise to the field of Galois theory. Charles Hermite first proved that e is transcendental, and Ferdinand von Lindemann, lindemanns proof was much simplified by Weierstrass, still further by David Hilbert, and has finally been made elementary by Adolf Hurwitz and Paul Gordan. The development of calculus in the 18th century used the set of real numbers without having defined them cleanly. The first rigorous definition was given by Georg Cantor in 1871, in 1874, he showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his first method was not his famous diagonal argument, the real number system can be defined axiomatically up to an isomorphism, which is described hereafter. Another possibility is to start from some rigorous axiomatization of Euclidean geometry, from the structuralist point of view all these constructions are on equal footing