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Johann Benedict Listing
Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician. Early life and education J. B. Listing was born in Frankfurt and died in Göttingen. He finished his studies at the University of Göttingen in 1834, and in 1839 he succeeded Wilhelm Weber as professor of physics. Career Listing first introduced the term "topology" to replace the older term "geometria situs" (also called sometimes "Analysis situs"), in a famous article published in 1847, although he had used the term in correspondence some years earlier. He (independently) discovered the properties of the Möbius strip, or half-twisted strip, at the same time (1858) as August Ferdinand Möbius, and went further in exploring the properties of strips with higher-order twists ( paradromic rings). He discovered topological invariants which came to be called Listing numbers. In ophthalmology, Listing's law describes an essential element of extraocular eye muscle coordination. In geodesy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frankfurt
Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the foreland of the Taunus on its namesake Main (river), Main, it forms a continuous conurbation with Offenbach am Main; Frankfurt Rhein-Main Regional Authority, its urban area has a population of over 2.7 million. The city is the heart of the larger Rhine-Main metropolitan region, which has a population of more than 5.8 million and is Germany's Metropolitan regions in Germany, second-largest metropolitan region after the Rhine-Ruhr metropolitan region, Rhine-Ruhr region and the List of EU metropolitan regions by GDP#2021 ranking of top four German metropolitan regions, fourth largest metropolitan region by GDP in the European Union (EU). Frankfurt is one of the ''de facto'' four main capitals of the European Union (alongside Brussels, Luxembourg Cit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a Surface (topology), surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Ancient Rome, Roman mosaics from the third century Common Era, CE. The Möbius strip is a orientability, non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a Knot (mathematics), knotted centerline. Any two embeddings with the same knot for the centerline and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1808 Births
Events January–March * January 1 ** The importation of slaves into the United States is formally banned, as the 1807 Act Prohibiting Importation of Slaves takes effect. However Americans still continue the slave trade by transporting Africans to Cuba and Brazil.. ** Sierra Leone becomes a British Crown Colony. * January 22 – Transfer of the Portuguese court to Brazil: John (Dom João), Prince Regent, and the Braganza royal family of Portugal arrive in their colony of Brazil in exile from the French occupation of their home kingdom. * January 26 – Rum Rebellion: On the 20th anniversary of the foundation of the colony of New South Wales, disgruntled military officers of the New South Wales Corps (the "Rum Corps") overthrow and imprison Governor William Bligh and seize control of the colony. * February 2 – French troops take Rome as part of the Napoleonic Wars. * February 6 – The ship '' Topaz'' (from Boston April 5, 1807, hunting seals) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Torsion (mechanics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a Set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of List of continuity-related mathematical topics, continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and Homotopy, homotopies. A property that is invariant under such deformations is a to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anna Airy
Anna Airy (6 June 1882 – 23 October 1964) was an English oil painter, pastel artist and etcher. She was one of the first women officially commissioned as a war artist and was recognised as one of the leading women artists of her generation. Early life and education Anna Airy was born on 6 June 1882 in Greenwich, London, the daughter of Anna ''(née'' Listing) and Wilfrid Airy, an engineer who worked on Orwell Park Observatory. Her paternal grandparents were Richarda and George Biddell Airy, the Astronomer Royal. Her maternal grandfather was Professor Johann Benedict Listing of the University of Göttingen and her parents met through her grandparents' European scientific connections and married in Göttingen on 27 April 1881. Airy's German mother died a fortnight after her birth and baby Anna was raised by two of her paternal aunts, Christabel and Annot Airy. Her aunts were both artists and encouraged her interest, as did her father who Airy later remembered promising "if I per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces ''Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the Gauss composition law, composition law, the Quadratic reciprocity, law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of Hypergeometric function, hypergeometric ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figure Of The Earth
In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for geography, astronomy and many other purposes. Several models with greater accuracy (including ellipsoid) have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns. Motivation Earth's topographic surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers, hydrographers, and geophysicists. While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated. The Pythagorean concept of a spherical Earth offers a simple surface that is easy to deal with mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geoid
The geoid ( ) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents (such as might be approximated with very narrow hypothetical canals). According to Carl Friedrich Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century. The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional space, 3D. It is called planetary geodesy when studying other astronomical body, astronomical bodies, such as planets or Natural satellite, circumplanetary systems. Geodynamics, Geodynamical phenomena, including crust (geology), crustal motion, tides, and polar motion, can be studied by designing global and national Geodetic control network, control networks, applying space geodesy and terrestrial geodetic techniques, and relying on Geodetic datum, datums and coordinate systems. Geodetic job titles include geodesist and geodetic surveyor. History Geodesy began in pre-scientific Classical antiquity, antiquity, so the very word geodesy comes from the Ancient Greek word or ''geodaisia'' (literally, "division of Earth"). Early ideas about t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ophthalmology
Ophthalmology (, ) is the branch of medicine that deals with the diagnosis, treatment, and surgery of eye diseases and disorders. An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a medical degree, a doctor specialising in ophthalmology must pursue additional postgraduate residency training specific to that field. In the United States, following graduation from medical school, one must complete a four-year residency in ophthalmology to become an ophthalmologist. Following residency, additional specialty training (or fellowship) may be sought in a particular aspect of eye pathology. Ophthalmologists prescribe medications to treat ailments, such as eye diseases, implement laser therapy, and perform surgery when needed. Ophthalmologists provide both primary and specialty eye care—medical and surgical. Most ophthalmologists participate in academic research on eye diseases at some point in their training and many inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilary Putnam
Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science. Outside philosophy, Putnam contributed to mathematics and computer science. Together with Martin Davis (mathematician), Martin Davis he developed the Davis–Putnam algorithm for the Boolean satisfiability problem and he helped demonstrate the unsolvability of Hilbert's tenth problem. Putnam applied equal scrutiny to his own philosophical positions as to those of others, subjecting each position to rigorous analysis until he exposed its flaws. As a result, he acquired a reputation for frequently changing his positions. In philosophy of mind, Putnam argued against the type physicalism, type-identity of mental and physical states based on his hypothesis of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Cambridge Conference Lectures Of 1898
''The'' is a grammatical article in English, denoting nouns that are already or about to be mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the most frequently used word in the English language; studies and analyses of texts have found it to account for seven percent of all printed English-language words. It is derived from gendered articles in Old English which combined in Middle English and now has a single form used with nouns of any gender. The word can be used with both singular and plural nouns, and with a noun that starts with any letter. This is different from many other languages, which have different forms of the definite article for different genders or numbers. Pronunciation In most dialects, "the" is pronounced as (with the voiced dental fricative followed by a schwa) when followed by a consonant sound, and as (homophone of the archaic pronoun ''thee' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
