1.
1830 in science
–
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.
1832 in architecture
–
The year 1832 in architecture involved some significant architectural events and new buildings. January - Theatre Royal, Wexford, Ireland Church of Our Saviour, Qaqortoq, cutlers Hall, Sheffield, England, designed by Samuel Worth and Benjamin Broomhead Taylor. Drapers Hall, Coventry, England, designed by Thomas Rickman, surgeons Hall, Edinburgh, Scotland, designed by William Henry Playfair. Replacement Old City Gaol, Bristol, England, designed by Richard Shackleton Pope, osgoode Hall, Toronto for The Law Society of Upper Canada, designed by John Ewart and W. W. Baldwin. Royal City of Dublin Hospital, Ireland, designed by Albert E. Murray, cathedral of the Holy Trinity, Gibraltar. Maderup Mølle, Funen, Denmark Théâtre des Folies-Dramatiques, Paris, the Mount, Sheffield, England, designed by William Flockton. Staines Bridge, designed by George Rennie, marlow Bridge, designed by William Tierney Clark. Bridge Real Ferdinando sul Garigliano, designed by Luigi Giura, George IV Bridge in Edinburgh, designed by Thomas Hamilton. St. Nicholas Greek Orthodox Church, New York City, USA Stirling New Bridge in Scotland, designed by Robert Stevenson, grand Prix de Rome, architecture, Jean-Arnoud Léveil
3.
Science
–
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
4.
Technology
–
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
5.
Thomas Bell (zoologist)
–
Thomas Bell FRS was an English zoologist, surgeon and writer, born in Poole, Dorset, England. Bell, like his mother Susan, took a keen interest in history which his mother also encouraged in his younger cousin Philip Henry Gosse. Bell left Poole in 1813 for his training as a surgeon in London. He combined two careers, becoming Professor of Zoology at Kings College London in 1836 and lecturing on anatomy at Guys Hospital and he became a fellow of the Royal College of Surgeons in 1844. He was President of the Linnean Society in 1858 and he was also entrusted with the specimens of Crustacea collected on the voyage. He was the authority in this field, his book British Stalke-eyed Crustacea is a masterwork and he supported the arrangements for publication of Zoology of the Voyage of H. M. S. In his seventieth year Bell retired to Selborne, where he took a keen interest in the amateur naturalist Gilbert White, in 1877 he published a new edition of Whites book The Natural History of Selborne. Bell died at Selborne in 1880, a Monograph of the Testudinata 1832–1836 – summarizes all the worlds turtles, living and extinct. The forty plates are by James de Carle Sowerby and Edward Lear, a History of the British Stalk-eyed Crustacea 1844–1853. John Van Voorst, Paternoster Row, London, a History of the British Stalk-eyed Crustacea, Internet Archive A Monograph of the Testudinata, Rare Book Room
6.
Turtle
–
Turtles are reptiles of the order Testudines characterised by a special bony or cartilaginous shell developed from their ribs and acting as a shield. Turtle may refer to the order as a whole or to fresh-water, the order Testudines includes both extant and extinct species. The earliest known members of this date from 157 million years ago, making turtles one of the oldest reptile groups. Of the 327 known species alive today, some are highly endangered, turtles are ectotherms—animals commonly called cold-blooded—meaning that their internal temperature varies according to the ambient environment. However, because of their metabolic rate, leatherback sea turtles have a body temperature that is noticeably higher than that of the surrounding water. Turtles are classified as amniotes, along with reptiles, birds. Like other amniotes, turtles breathe air and do not lay eggs underwater, Chelonia is based on the Greek word χελώνη chelone tortoise, turtle, also denoting armor or interlocking shields, testudines, on the other hand, is based on the Latin word testudo tortoise. Turtle may either refer to the order as a whole, or to particular turtles that make up a form taxon that is not monophyletic, the meaning of the word turtle differs from region to region. In North America, all chelonians are commonly called turtles, including terrapins, in Great Britain, the word turtle is used for sea-dwelling species, but not for tortoises. The term tortoise usually refers to any land-dwelling, non-swimming chelonian, most land-dwelling chelonians are in the Testudinidae family, only one of the 14 extant turtle families. Terrapin is used to describe several species of small, edible, hard-shell turtles, typically found in brackish waters. Some languages do not have this distinction, as all of these are referred to by the same name, for example, in Spanish, the word tortuga is used for turtles, tortoises, and terrapins. A sea-dwelling turtle is tortuga marina, a freshwater species tortuga de río, the largest living chelonian is the leatherback sea turtle, which reaches a shell length of 200 cm and can reach a weight of over 900 kg. Freshwater turtles are generally smaller, but with the largest species, the Asian softshell turtle Pelochelys cantorii, a few individuals have been reported up to 200 cm. This dwarfs even the better-known alligator snapping turtle, the largest chelonian in North America and they became extinct at the same time as the appearance of man, and it is assumed humans hunted them for food. The only surviving giant tortoises are on the Seychelles and Galápagos Islands and can grow to over 130 cm in length, the largest ever chelonian was Archelon ischyros, a Late Cretaceous sea turtle known to have been up to 4.6 m long. The smallest turtle is the speckled padloper tortoise of South Africa and it measures no more than 8 cm in length and weighs about 140 g. Two other species of turtles are the American mud turtles
7.
Isidore Geoffroy Saint-Hilaire
–
Isidore Geoffroy Saint-Hilaire was a French zoologist and an authority on deviation from normal structure. In 1854 he coined the term éthologie and he was born in Paris, the son of Étienne Geoffroy Saint-Hilaire. He was elected a member of the French Academy of Sciences in 1833, was in 1837 appointed to act as deputy for his father at the faculty of sciences in Paris, during the following year he was sent to Bordeaux to organize a similar faculty there. In 1854 he founded the Société zoologique dacclimatation, of which he served as president. He conducted investigations of omphalosites, celosomia, hermaphroditism, etc. and is credited with introducing the term teratologie, from 1832 to 1837 he published his great teratological work, Histoire générale et particulière des anomalies de l’organisation chez l’homme et les animaux. Besides the above-mentioned work, he wrote, Histoire générale et particulière des anomalies de l’organisation chez l’homme et les animaux, acclimatation et domestication des animaux utiles. Lettres sur les substances alimentaires et particulièrement sur la viande de cheval, Histoire naturelle générale des règnes organiques, which was not quite completed. He was also the author of papers on zoology, comparative anatomy. List of Chairs of the Muséum national dhistoire naturelle This article incorporates text from a now in the public domain, Chisholm, Hugh
8.
Teratology
–
Teratology is the study of abnormalities of physiological development. The related term developmental toxicity includes all manifestations of abnormal development that are caused by environmental insult and these may include growth retardation, delayed mental development or other congenital disorders without any structural malformations. Teratogens are substances that may cause birth defects via an effect on an embryo or foetus. The term teratology stems from the Greek τέρας teras, meaning monster or marvel, and λόγος logos, meaning the word or, more loosely, as early as the 17th century, teratology referred to a discourse on prodigies and marvels of anything so extraordinary as to seem abnormal. In the 19th century it acquired a more closely related to biological deformities. Currently, its most instrumental meaning is that of the study of teratogenesis. Historically, people have used many pejorative terms to describe/label cases of significant physical malformations, in the 1960s David W. Smith of the University of Washington Medical School, popularized the term teratology. With the growth of understanding of the origins of birth defects, the field of teratology as of 2015 overlaps with other fields of science, including biology, embryology. Until the 1940s teratologists regarded birth defects as primarily hereditary, in 1941 the first well-documented cases of environmental agents being the cause of severe birth defects were reported. Along with this new awareness of the in utero vulnerability of the mammalian embryo came the development and refinement of The Six Principles of Teratology which are still applied today. These principles of teratology were put forth by Jim Wilson in 1959 and in his monograph Environment, susceptibility to teratogenesis varies with the developmental stage at the time of exposure to an adverse influence. There are critical periods of susceptibility to agents and organ systems affected by these agents, teratogenic agents act in specific ways on developing cells and tissues to initiate sequences of abnormal developmental events. The access of adverse influences to developing tissues depends on the nature of the influence, there are four manifestations of deviant development. Manifestations of deviant development increase in frequency and degree as dosage increases from the No Observable Adverse Effect Level to a dose producing 100% Lethality, studies designed to test the teratogenic potential of environmental agents use animal model systems. Early teratologists exposed pregnant animals to environmental agents and observed the fetuses for gross visceral and skeletal abnormalities. While this is part of the teratological evaluation procedures today. Genetically modified mice are used for this purpose. In addition, pregnancy registries are large, prospective studies that monitor exposures women receive during their pregnancies and these studies provide information about possible risks of medications or other exposures in human pregnancies
9.
Pierre Jean Robiquet
–
Pierre Jean Robiquet was a French chemist. He laid founding work in identifying amino acids, the building blocks of proteins. He was at first a pharmacist in the French armies during the French Revolution years and became a professor at the École de pharmacie in Paris, some of these discoveries were made in collaboration with other scientists. Distinguished with the order of the Légion dHonneur, in the fall of 1805, Robiquet, then a young help working in the laboratory of Louis Nicolas Vauquelin, started analyses, with what rudimentary methods were then available, with asparagus juice. Duly convinced this is something new, they call this matter asparagin. Asparagine will turn out to be one of the 22 amino acids that build-up all living matter on earth, progress in isolating the other amino acids will be very slow, with less than a handful in total during the whole 19th century. Even until the middle of 19th century, all used for colouring cloth were natural substances. Furthermore, many lacked stability through washing or exposure to sunlight and its extraction was variable and complicated, and dependent on the availability of the very specific type of shell from which it was extracted. Another type of red dye used from times immemorial was obtained from madder root in Central Asia and Egypt. Cloth dyed with madder root pigment was found in the tomb of the Pharaoh Tutankhamun and in the ruins of Pompeii, in the Middle Ages, Charlemagne encouraged madder cultivation. It grew well in the soils of the Netherlands and became an important part of the local economy. By 1804, the English dye maker George Field had introduced new techniques known as lake madder and it is one of the most effective orally-administered opioid analgesics and has a wide safety margin. It is from 8 to 12 percent of the strength of morphine in most people, differences in metabolism can change this figure as can other medications, depending on its route of administration. While codeine can still be extracted from opium, its original source. Thus, in 1809, Robiquet extracts from liquorice root a sweetish matter which he dubs glycyrrhizine, from Glycirrhiza, Robiquet likewise analysed a variety of animal tissues. In the frame of that investigation, Robiquet in addition evidences the presence of uric acid within insects feeding on plant tissues. Over a period of fifteen years, Pierre Robiquet will also conduct a series of investigations on bitter almonds oil. In 1816, together with Jean-Jacques Colin, they obtain a new component which they call éther hydrochlorique and this discovery was opening the door to the huge family of aromatic molecules, that are based on the cyclic 6 carbon benzenoic structure
10.
Analgesic
–
An analgesic or painkiller is any member of the group of drugs used to achieve analgesia, relief from pain. Analgesic drugs act in various ways on the peripheral and central nervous systems and they are distinct from anesthetics, which temporarily affect, and in some instances completely eliminate, sensation. Analgesics include paracetamol, the nonsteroidal anti-inflammatory drugs such as the salicylates, when choosing analgesics, the severity and response to other medication determines the choice of agent, the World Health Organization pain ladder specifies mild analgesics as its first step. Topical nonsteroidal anti-inflammatory drugs provided pain relief in common such as muscle sprains. Since the side effects are also lesser, topical preparations could be preferred over oral medications in these conditions, each different type of analgesic has its own associated side effects. Drugs for pain are typically classified by chemical structure and they may also be classified in other ways. Sometimes they are classified by use for classes of medical condition. Other times they are sorted by the needs of populations who would use them. They might be listed by availability in an area, perhaps to prevent recommending a drug which is illegal in one place even if it is easily available elsewhere. Paracetamol, also known as acetaminophen or APAP, is a used to treat pain. It is typically used for mild to moderate pain, in combination with opioid pain medication, paracetamol is used for more severe pain such as cancer pain and after surgery. It is typically used either by mouth or rectally but is also available intravenously, effects last between two and four hours. Paracetamol is classified as a mild analgesic, paracetamol is generally safe at recommended doses. Nonsteroidal anti-inflammatory drugs, are a class that groups together drugs that provide analgesic and antipyretic effects. The most prominent members of group of drugs, aspirin. These drugs have been derived from NSAIDs, the cyclooxygenase enzyme inhibited by NSAIDs was discovered to have at least 2 different versions, COX1 and COX2. Research suggested most of the effects of NSAIDs to be mediated by blocking the COX1 enzyme. Thus, the COX2 inhibitors were developed to inhibit only the COX2 enzyme and these drugs are equally effective analgesics when compared with NSAIDs, but cause less gastrointestinal hemorrhage in particular
11.
Functional group
–
In organic chemistry, functional groups are specific groups of atoms or bonds within molecules that are responsible for the characteristic chemical reactions of those molecules. The same functional group will undergo the same or similar chemical reaction regardless of the size of the molecule it is a part of, however, its relative reactivity can be modified by other functional groups nearby. The atoms of functional groups are linked to other and to the rest of the molecule by covalent bonds. Any subgroup of atoms of a compound also may be called a radical, and if a covalent bond is broken homolytically, Functional groups can also be charged, e. g. in carboxylate salts, which turns the molecule into a polyatomic ion or a complex ion. Complexation and solvation is also caused by interactions of functional groups. In the common rule of thumb like dissolves like, it is the shared or mutually well-interacting functional groups give rise to solubility. For example, sugar dissolves in water because both share the functional group and hydroxyls interact strongly with each other. Combining the names of groups with the names of the parent alkanes generates what is termed a systematic nomenclature for naming organic compounds. In traditional nomenclature, the first carbon atom after the carbon that attaches to the group is called the alpha carbon, the second, beta carbon. IUPAC conventions call for numeric labeling of the position, e. g. 4-aminobutanoic acid, in traditional names various qualifiers are used to label isomers, for example isopropanol is an isomer is n-propanol. The following is a list of functional groups. In the formulas, the symbols R and R usually denote an attached hydrogen, or a side chain of any length. Functional groups, called hydrocarbyl, that only carbon and hydrogen. Each one differs in type of reactivity, there are also a large number of branched or ring alkanes that have specific names, e. g. tert-butyl, bornyl, cyclohexyl, etc. Hydrocarbons may form charged structures, positively charged carbocations or negative carbanions, examples are tropylium and triphenylmethyl cations and the cyclopentadienyl anion. Haloalkanes are a class of molecule that is defined by a carbon–halogen bond and this bond can be relatively weak or quite stable. In general, with the exception of fluorinated compounds, haloalkanes readily undergo nucleophilic substitution reactions or elimination reactions, the substitution on the carbon, the acidity of an adjacent proton, the solvent conditions, etc. all can influence the outcome of the reactivity. Compounds that contain nitrogen in this category may contain C-O bonds, compounds that contain sulfur exhibit unique chemistry due to their ability to form more bonds than oxygen, their lighter analogue on the periodic table
12.
Radical (chemistry)
–
In chemistry, a radical is an atom, molecule, or ion that has an unpaired valence electron. Most radicals are reasonably stable only at low concentrations in inert media or in a vacuum. A notable example of a radical is the hydroxyl radical. Two other examples are triplet oxygen and triplet carbene which have two unpaired electrons, free radicals may be created in a number of ways, including synthesis with very dilute or rarefied reagents, reactions at very low temperatures, or breakup of larger molecules. The latter can be affected by any process that puts energy into the parent molecule, such as ionizing radiation, heat, electrical discharges, electrolysis. Radicals are intermediate stages in many chemical reactions, free radicals play an important role in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical processes. In living organisms, the free radicals superoxide and nitric oxide and their reaction products regulate many processes, such as control of vascular tone and they also play a key role in the intermediary metabolism of various biological compounds. Such radicals can even be messengers in a process dubbed redox signaling, a radical may be trapped within a solvent cage or be otherwise bound. The qualifier free was then needed to specify the unbound case, following recent nomenclature revisions, a part of a larger molecule is now called a functional group or substituent, and radical now implies free. However, the old nomenclature may still appear in some books, the term radical was already in use when the now obsolete radical theory was developed. Louis-Bernard Guyton de Morveau introduced the phrase radical in 1785 and the phrase was employed by Antoine Lavoisier in 1789 in his Traité Élémentaire de Chimie, a radical was then identified as the root base of certain acids. Historically, the radical in radical theory was also used for bound parts of the molecule. These are now called functional groups, for example, methyl alcohol was described as consisting of a methyl radical and a hydroxyl radical. In a modern context the first organic free radical identified was triphenylmethyl radical and this species was discovered by Moses Gomberg in 1900 at the University of Michigan USA. In 1933 Morris Kharash and Frank Mayo proposed that free radicals were responsible for anti-Markovnikov addition of hydrogen bromide to allyl bromide. It should be noted that the electron of the breaking bond also moves to pair up with the attacking radical electron. Free radicals also take part in addition and radical substitution as reactive intermediates. Chain reactions involving free radicals can usually be divided into three distinct processes and these are initiation, propagation, and termination
13.
Carl Reichenbach
–
Baron Dr. Carl Ludwig von Reichenbach was a notable chemist, geologist, metallurgist, naturalist, industrialist and philosopher, and a member of the prestigious Prussian Academy of Sciences. He is best known for his discoveries of several products of economic importance, extracted from tar, such as eupione, waxy paraffin, pittacal. He also dedicated himself in his last years to research an unproved field of energy combining electricity, magnetism and heat, emanating from all living things, Reichenbach was educated at the University of Tübingen, where he obtained the degree of doctor of philosophy. At the age of 16 he conceived the idea of establishing a new German state in one of the South Sea Islands, Reichenbach conducted original scientific investigations in many areas. The first geological monograph which appeared in Austria was his Geologische Mitteilungen aus Mähren, under the name of eupione, Reichenbach included the mixture of hydrocarbon oils now known as waxy paraffin or coal oils. His reasoning was that meteorites and planets are the same, and no matter the size of the meteorite and this was deemed conclusive by the scientific community in the 19th century. In 1839 Von Reichenbach retired from industry and entered upon an investigation of the pathology of the nervous system. He studied neurasthenia, somnambulism, hysteria and phobia, crediting reports that conditions were affected by the moon. After interviewing many patients he ruled out many causes and cures, to this vitalist manifestation he gave the name Odic force. Reichenbach and his Odic force are referred to in the game Amnesia, regarding personal names, Freiherr is a former title, which is now legally a part of the last name. The feminine forms are Freifrau and Freiin, paranormal Site Karl Ludwig von Reichenbach. Stadt Stuttgart Researches on Magnetism, Electricity, Heat and Light in their relations to Vital Forces
14.
Circumnavigation
–
Circumnavigation means to travel all the way around the entire planet, or an island, or continent. This article is concerned with circumnavigation of the Earth, the first known circumnavigation of Earth was the Magellan-Elcano expedition, which sailed from Seville, Spain, in 1519 and returned in 1522 after crossing the Atlantic, Pacific and Indian oceans. The word circumnavigation is a formed from the verb circumnavigate, from the past participle of the Latin verb circumnavigare. If a person walks completely around either Pole, they cross all meridians, the trajectory of a true circumnavigation forms a continuous loop on the surface of Earth separating two halves of comparable area. A basic definition of a global circumnavigation would be a route which covers roughly a great circle, in practice, people use different definitions of world circumnavigation to accommodate practical constraints, depending on the method of travel. The first single voyage of global circumnavigation was that of the ship Victoria and it was a Castilian voyage of discovery, led initially by Ferdinand Magellan between 1519 and 1521, and then by the Basque Juan Sebastián Elcano from 1521 to 1522. It then continued across the Pacific discovering a number of islands on its way, Elcano and a small group of 18 men were actually the only members of the expedition to make the full circumnavigation. However, traveling west from Europe, in 1521, Magellan reached a region of Southeast Asia, Magellan thereby achieved a nearly complete personal circumnavigation of the globe for the first time in history. In 1577, Elizabeth I sent Francis Drake to start an expedition against the Spanish along the Pacific coast of the Americas, Drake set out from Plymouth, England in November 1577, aboard Pelican, which Drake renamed Golden Hind mid-voyage. In June 1579, Drake landed somewhere north of Spains northern-most claim in Alta California, Drake completed the second circumnavigation of the world in September 1580, becoming the first commander to lead an entire circumnavigation. For the wealthy, long voyages around the world, such as was done by Ulysses S. Grant, became possible in the 19th century, however, it was later improvements in technology and rising incomes that made such trips relatively common. The nautical global circumnavigation record is held by a wind-powered vessel. It can be seen that the route roughly approximates a great circle, in yacht racing, a round-the-world route approximating a great circle would be quite impractical, particularly in a non-stop race where use of the Panama and Suez Canals would be impossible. The second map on the shows the route of the Vendée Globe round-the-world race in red. It can be seen that the route does not pass through any pairs of antipodal points and it is allowed to have one single waypoint to lengthen the calculated track. The voyage followed the North Atlantic Ocean, Equator, South Atlantic Ocean, Southern Ocean, South Atlantic Ocean, Equator, since the advent of world cruises in 1922, by Cunards Laconia, thousands of people have completed circumnavigations of the globe at a more leisurely pace. Typically, these voyages begin in New York City or Southampton, routes vary, either travelling through the Caribbean and then into the Pacific Ocean via the Panama Canal, or around Cape Horn. From there ships usually make their way to Hawaii, the islands of the South Pacific, Australia, New Zealand, then northward to Hong Kong, South East Asia, and India
15.
Algebra
–
Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols, as such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine, abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are unknown or allowed to take on many values. For example, in x +2 =5 the letter x is unknown, in E = mc2, the letters E and m are variables, and the letter c is a constant, the speed of light in a vacuum. Algebra gives methods for solving equations and expressing formulas that are easier than the older method of writing everything out in words. The word algebra is used in certain specialized ways. A special kind of object in abstract algebra is called an algebra. A mathematician who does research in algebra is called an algebraist, the word algebra comes from the Arabic الجبر from the title of the book Ilm al-jabr wal-muḳābala by Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the century, from either Spanish, Italian. It originally referred to the procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century, the word algebra has several related meanings in mathematics, as a single word or with qualifiers. As a single word without an article, algebra names a broad part of mathematics, as a single word with an article or in plural, an algebra or algebras denotes a specific mathematical structure, whose precise definition depends on the author. Usually the structure has an addition, multiplication, and a scalar multiplication, when some authors use the term algebra, they make a subset of the following additional assumptions, associative, commutative, unital, and/or finite-dimensional. In universal algebra, the word refers to a generalization of the above concept. With a qualifier, there is the distinction, Without an article, it means a part of algebra, such as linear algebra, elementary algebra. With an article, it means an instance of some abstract structure, like a Lie algebra, sometimes both meanings exist for the same qualifier, as in the sentence, Commutative algebra is the study of commutative rings, which are commutative algebras over the integers
16.
Group theory
–
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra, linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is central to public key cryptography. The first class of groups to undergo a systematic study was permutation groups, given any set X and a collection G of bijections of X into itself that is closed under compositions and inverses, G is a group acting on X. If X consists of n elements and G consists of all permutations, G is the symmetric group Sn, in general, an early construction due to Cayley exhibited any group as a permutation group, acting on itself by means of the left regular representation. In many cases, the structure of a group can be studied using the properties of its action on the corresponding set. For example, in this way one proves that for n ≥5 and this fact plays a key role in the impossibility of solving a general algebraic equation of degree n ≥5 in radicals. The next important class of groups is given by matrix groups, here G is a set consisting of invertible matrices of given order n over a field K that is closed under the products and inverses. Such a group acts on the vector space Kn by linear transformations. In the case of groups, X is a set, for matrix groups. The concept of a group is closely related with the concept of a symmetry group. The theory of groups forms a bridge connecting group theory with differential geometry. A long line of research, originating with Lie and Klein, the groups themselves may be discrete or continuous. Most groups considered in the first stage of the development of group theory were concrete, having been realized through numbers, permutations, or matrices. It was not until the nineteenth century that the idea of an abstract group as a set with operations satisfying a certain system of axioms began to take hold. A typical way of specifying an abstract group is through a presentation by generators and relations, a significant source of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory
17.
Galois theory
–
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, originally, Galois used permutation groups to describe how the various roots of a given polynomial equation are related to each other. The modern approach to Galois theory, developed by Richard Dedekind, Leopold Kronecker and Emil Artin, among others, further abstraction of Galois theory is achieved by the theory of Galois connections. Further, it gives a clear, and often practical. Galois theory also gives an insight into questions concerning problems in compass. It gives an elegant characterisation of the ratios of lengths that can be constructed with this method, for instance, = x2 – x + ab, where 1, a + b and ab are the elementary polynomials of degree 0,1 and 2 in two variables. This was first formalized by the 16th-century French mathematician François Viète, in Viètes formulas, the first person who understood the general doctrine of the formation of the coefficients of the powers from the sum of the roots and their products. He was the first who discovered the rules for summing the powers of the roots of any equation, see Discriminant, Nature of the roots for details. This solution was then rediscovered independently in 1535 by Niccolò Fontana Tartaglia, Cardano then extended this to numerous other cases, using similar arguments, see more details at Cardanos method. After the discovery of Ferros work, he felt that Tartaglias method was no longer secret and his student Lodovico Ferrari solved the quartic polynomial, his solution was also included in Ars Magna. With the benefit of modern notation and complex numbers, the formulae in this book do work in the general case and it was Rafael Bombelli who managed to understand how to work with complex numbers in order to solve all forms of cubic equation. Crucially, however, he did not consider composition of permutations, lagranges method did not extend to quintic equations or higher, because the resolvent had higher degree. The quintic was almost proven to have no general solutions by radicals by Paolo Ruffini in 1799, whose key insight was to use permutation groups, not just a single permutation. This group was always solvable for polynomials of degree four or less, but not always so for polynomials of degree five and greater, prior to this publication, Liouville announced Galois result to the Academy in a speech he gave on 4 July 1843. According to Allan Clark, Galoiss characterization dramatically supersedes the work of Abel, Galois theory was notoriously difficult for his contemporaries to understand, especially to the level where they could expand on it. For example, in his 1846 commentary, Liouville completely missed the core of Galois method. Joseph Alfred Serret who attended some of Liouvilles talks, included Galois theory in his 1866 of his textbook Cours dalgèbre supérieure, serrets pupil, Camille Jordan had an even better understanding reflected in his 1870 book Traité des substitutions et des équations algébriques. Outside France Galois theory remained more obscure for a longer period, in Britain, Cayley failed to grasp its depth and popular British algebra textbooks didnt even mention Galois theory until well after the turn of the century
18.
Peter Gustav Lejeune Dirichlet
–
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
19.
Fermat's Last Theorem
–
In number theory, Fermats Last Theorem states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n =1 and n =2 have been known to have many solutions since antiquity. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, the unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. The Pythagorean equation, x2 + y2 = z2, has an number of positive integer solutions for x, y, and z. Around 1637, Fermat wrote in the margin of a book that the general equation an + bn = cn had no solutions in positive integers. Although he claimed to have a proof of his conjecture, Fermat left no details of his proof. His claim was discovered some 30 years later, after his death and this claim, which came to be known as Fermats Last Theorem, stood unsolved in mathematics for the following three and a half centuries. The claim eventually became one of the most notable unsolved problems of mathematics, attempts to prove it prompted substantial development in number theory, and over time Fermats Last Theorem gained prominence as an unsolved problem in mathematics. With the special case n =4 proved, it suffices to prove the theorem for n that are prime numbers. Over the next two centuries, the conjecture was proved for only the primes 3,5, and 7, in the mid-19th century, Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Around 1955, Japanese mathematicians Goro Shimura and Yutaka Taniyama suspected a link might exist between elliptic curves and modular forms, two different areas of mathematics. Known at the time as the Taniyama–Shimura-Weil conjecture, and as the modularity theorem, it stood on its own and it was widely seen as significant and important in its own right, but was widely considered completely inaccessible to proof. In 1984, Gerhard Frey noticed an apparent link between the modularity theorem and Fermats Last Theorem and this potential link was confirmed two years later by Ken Ribet, who gave a conditional proof of Fermats Last Theorem that depended on the modularity theorem. On hearing this, English mathematician Andrew Wiles, who had a fascination with Fermats Last Theorem. In 1993, after six years working secretly on the problem, Wiless paper was massive in size and scope. A flaw was discovered in one part of his paper during peer review and required a further year and collaboration with a past student, Richard Taylor. As a result, the proof in 1995 was accompanied by a second smaller joint paper to that effect
20.
Non-Euclidean geometry
–
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry. In the latter case one obtains hyperbolic geometry and elliptic geometry, when the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry. The essential difference between the geometries is the nature of parallel lines. In hyperbolic geometry, by contrast, there are many lines through A not intersecting ℓ, while in elliptic geometry. In elliptic geometry the lines curve toward each other and intersect, the debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclids work Elements was written. In the Elements, Euclid began with a number of assumptions. Other mathematicians have devised simpler forms of this property, regardless of the form of the postulate, however, it consistently appears to be more complicated than Euclids other postulates,1. To draw a line from any point to any point. To produce a straight line continuously in a straight line. To describe a circle with any centre and distance and that all right angles are equal to one another. For at least a thousand years, geometers were troubled by the complexity of the fifth postulate. Many attempted to find a proof by contradiction, including Ibn al-Haytham, Omar Khayyám, Nasīr al-Dīn al-Tūsī and these theorems along with their alternative postulates, such as Playfairs axiom, played an important role in the later development of non-Euclidean geometry. These early attempts did, however, provide some early properties of the hyperbolic and elliptic geometries. Another example is al-Tusis son, Sadr al-Din, who wrote a book on the subject in 1298, based on al-Tusis later thoughts and he essentially revised both the Euclidean system of axioms and postulates and the proofs of many propositions from the Elements. His work was published in Rome in 1594 and was studied by European geometers and he finally reached a point where he believed that his results demonstrated the impossibility of hyperbolic geometry. His claim seems to have based on Euclidean presuppositions, because no logical contradiction was present. In this attempt to prove Euclidean geometry he instead unintentionally discovered a new viable geometry, in 1766 Johann Lambert wrote, but did not publish, Theorie der Parallellinien in which he attempted, as Saccheri did, to prove the fifth postulate. He worked with a figure that today we call a Lambert quadrilateral and he quickly eliminated the possibility that the fourth angle is obtuse, as had Saccheri and Khayyam, and then proceeded to prove many theorems under the assumption of an acute angle