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August Ferdinand Möbius
August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer. Early life and education Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mother's side from religious reformer Martin Luther. He was home-schooled until he was 13, when he attended the college in Schulpforta in 1803, and studied there, graduating in 1809. He then enrolled at the University of Leipzig, where he studied astronomy under the mathematician and astronomer Karl Mollweide.August Ferdinand Möbius, The MacTutor History of Mathematics archive History.mcs.st-andrews.ac.uk. Retrieved on 2017-04-26. In 1813, he began to study astronomy under mathematician |
Schulpforta
Pforta, or Schulpforta, is a school located in Pforta monastery, a former Cistercian monastery (1137–1540), near Naumburg on the Saale River in the German state of Saxony-Anhalt. The site has been a school since the 16th century. Notable past alumni include the mathematician August Ferdinand Möbius, the historian Leopold von Ranke, and the philosopher Friedrich Nietzsche. Today, it is a well-known public boarding school for academically gifted children, called Landesschule Pforta. It is coeducational and teaches around 300 high school students. Pforta is proposed for inscription in the World Heritage List as one component of the German nomination Naumburg Cathedral and the High Medieval Cultural Landscape of the Rivers Saale and Unstrut. History Monastery The abbey was at first situated in Schmölln on the Sprotta, near Altenburg. In 1127, Count Bruno of Pleissengau founded a Benedictine monastery there and endowed it with 1,100 hides of land. This foundation not being s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Inversion Formula
In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius. A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra. Statement of the formula The classic version states that if and are arithmetic functions satisfying : g(n)=\sum_f(d)\quad\textn\ge 1 then :f(n)=\sum_\mu(d)g\left(\frac\right)\quad\textn\ge 1 where is the Möbius function and the sums extend over all positive divisors of (indicated by d \mid n in the above formulae). In effect, the original can be determined given by using the inversion formula. The two sequences are said to be Möbius transforms of each other. The formula is also correct if and are funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johann Benedict Listing
Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician. J. B. Listing was born in Frankfurt and died in Göttingen. He 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 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. Peirce, C. S., 1992, '' Reasoning and the Logic of Things: The Cambridge Conference Lectures of 1898'', edited with introduction by Kenneth Laine Ketner and with commentary by Hilary Putnam, who discusses Listing numbers starting on page 99. It is currently difficult to find anything online about Listing nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the three-dimensional space and the ''Euclidean plane'' (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of '' proving'' all properties of the space as theorems, by starting from a few fundamental properties, called ''postulates'', which either were considered as evident (for example, there is exactly one straight line passing through two points), or seemed impossible to prove (paral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map f:X\rightarrow Y. The precise meaning of "structure-preserving" depends on the kind of mathematical structure of which X and Y are instances. In the terminology of category theory, a structure-preserving map is called a morphism. The fact that a map f:X\rightarrow Y is an embedding is often indicated by the use of a "hooked arrow" (); thus: f : X \hookrightarrow Y. (On the other hand, this notation is sometimes reserved for inclusion maps.) Given X and Y, several different embeddings of X in Y may be possible. In many cases of interest there is a standard (or "canonical") embedding, like those of the natural numbers in the integers, the integers in the rational numbers, the rational numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-orientable
In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space. Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theodor Möbius
Theodor Möbius (June 22, 1821 Leipzig - April 25, 1890) was a German philologist who specialized in Germanic studies. Biography He was a son of German mathematician August Ferdinand Möbius. He studied at the Universities of Leipzig (1840–42) and Berlin (1842-43), receiving his doctorate in 1844 at Leipzig. From 1845 to 1861, he was an assistant, then later curator, at the university library. He earned his habilitation at Leipzig in 1852 with the thesis ''Über die ältere isländische Saga'', and in 1859 became a professor of Scandinavian languages and literature there. In 1865, he accepted a similar position at Kiel. He edited many old Norse works. Selected works * ''Catalogus librorum islandicorum et norvegicorum ætatis mediæ editorum versorum illustratorum : Skáldatal sive Poetarum recensus Eddæ upsaliensis'', Lipsiæ : Apud W. Engelmannum, 1856. * ''Altnordisches Glossar : wörterbuch zu einer Auswahl alt-isländischer und alt-norwegischer Prosatexte'', Leipzig : B. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Göttingen Observatory
Göttingen Observatory (''Universitätssternwarte Göttingen'' (Göttingen University Observatory) or ''königliche Sternwarte Göttingen'' (Royal Observatory Göttingen)) is a German astronomical observatory located in Göttingen, Lower Saxony, Germany. History In 1802, George III of the United Kingdom, who was also the prince-elector of Hanover, allocated 22,680 thalers for a new observatory. The plans were developed, like many of the university's buildings, by Georg Heinrich Borheck. Construction was delayed by the French Revolutionary Wars and extended from 1803 until 1816. At the time, the building was on the outskirts of Göttingen, to ensure an unobstructed view of the night sky. Carl Friedrich Gauss became the first director of the Observatory, and lived there between 1815 and 1855. Gauss arranged for the installation of two meridian circles (produced by Johann Georg Repsold and Georg Friedrich von Reichenbach in 1818 and 1819. Gauss was succeeded by Wilhelm Weber and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plume (publisher)
Plume is a publishing company in the United States, founded in 1970 as the trade paperback imprint of New American Library. Today it is a division of Penguin Group, with a backlist of approximately 700 titles. References External links Plume - Penguin Books USA Pearson plc Book publishing companies based in New York (state) Publishing companies established in 1970 {{Publish-corp-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Luther
Martin Luther (; ; 10 November 1483 – 18 February 1546) was a German priest, theologian, author, hymnwriter, and professor, and Augustinian friar. He is the seminal figure of the Protestant Reformation and the namesake of Lutheranism. Luther was ordained to the priesthood in 1507. He came to reject several teachings and practices of the Roman Catholic Church; in particular, he disputed the view on indulgences. Luther proposed an academic discussion of the practice and efficacy of indulgences in his ''Ninety-five Theses'' of 1517. His refusal to renounce all of his writings at the demand of Pope Leo X in 1520 and the Holy Roman Emperor Charles V at the Diet of Worms in 1521 resulted in his excommunication by the pope and condemnation as an outlaw by the Holy Roman Emperor. Luther taught that salvation and, consequently, eternal life are not earned by good deeds but are received only as the free gift of God's grace through the believer's fait ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either observational (by analyzing the data) or theoretical astronomy. Examples of topics or fields astronomers study include planetary science, solar astronomy, the origin or evolution of stars, or the formation of galaxies. A related but distinct subject is physical cosmology, which studies the Universe as a whole. Types Astronomers usually fall under either of two main types: observational and theoretical. Observational astronomers make direct observations of celestial objects and analyze the data. In contrast, theoretical astronomers create and investigate models of things that cannot be observed. Because it takes millions to billions of years for a system of stars or a galaxy to complete a life cycle, astronomers must observe snapsh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
