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List Of Things Named After Euclid
This is a list of topics named after the Greek mathematician Euclid. Mathematics Number theory * Euclidean algorithm ** Extended Euclidean algorithm * Euclidean division * Euclid–Euler theorem * Euclid number * Euclid's lemma * Euclid's orchard * Euclid–Mullin sequence * Euclid's theorem Algebra * Euclidean domain * Euclidean field Geometry * Euclidean group * Euclidean geometry **Non-Euclidean geometry * Euclid's formula * Euclidean distance **Euclidean distance matrix * Euclidean space **Pseudo-Euclidean space * Euclidean vector * Euclidean relation * Euclidean topology * Euclid's fifth postulate Other * Euclid's Elements * Euclid's Optics * Euclid (spacecraft) * Euclid, Ohio Euclid, Minnesota * Euclidean rhythm a term coined by Godfried Toussaint in his 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms" * Euclid (computer program) * Euclid (programming language) * Euclid, a supercomputer built by the fictional character Maximillian Cohen in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by Greek culture and the Greek language. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations. Origins of Greek mathematics The origin of Greek mathematics is not well documented. The earliest advanced civilizations in Greece and in Europe were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Rhythm
The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms".The Euclidean algorithm generates traditional musical rhythms by G. T. Toussaint, ''Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science'', Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56. The of two numbers is used rhythmically giving the number of beats ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid, Minnesota
Euclid is an unincorporated community in Polk County, Minnesota, United States. It is situated on U.S. Route 75, north of Crookston. Euclid has a post office with ZIP code 56722. History A post office called Euclid has been in operation since 1879. The community was named after Euclid Avenue, a main boulevard of Cleveland, Ohio. Population Euclid has a population of 132, of whom 54.5% are male and 45.5% female. The average age is estimated at 48.5. There are two main ethnicities, white and Hispanic, which are respectively 97% and 3% of the population. The average number of residents per household A household consists of two or more persons who live in the same dwelling. It may be of a single family or another type of person group. The household is the basic unit of analysis in many social, microeconomic and government models, and is im ... is estimated at 2.32, with an estimated 57 households in the area. References Former municipalities in Minnesota Unincorp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid, Ohio
Euclid is a city in Cuyahoga County, Ohio, United States. It is an inner ring suburb of Cleveland. As of the 2020 census, the city had a total population of 49,692. History The City of Euclid was originally a part of Euclid Township, first mapped in 1796 and named for Euclid of Alexandria, the ancient Greek mathematician. The first sparse settlement in the township began in 1798, with major settlement beginning in the spring of 1804. The first settlers in what is now the City of Euclid were Joseph Burke, David Dille and William Coleman, and their families. Following the Civil War the lake plain of Euclid Township was known for numerous excellent vineyards. Euclid Village incorporated out of the northeast portion of the township in 1903. It developed as an industrial center in the early 20th century, and became a city in 1930. Geography Euclid is located at (41.595563, -81.519176). According to the United States Census Bureau, the city has a total area of , of which is land ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid (spacecraft)
Euclid is a visible to near-infrared space telescope currently under development by the European Space Agency (ESA) and the Euclid Consortium. The objective of the Euclid mission is to better understand dark energy and dark matter by accurately measuring the accelerating universe, acceleration of the universe. To achieve this, the Korsch telescope, Korsch-type telescope will measure the shapes of galaxies at varying distances from Earth and investigate the relationship between distance and redshift. Dark energy is generally accepted as contributing to the increased acceleration of the expanding universe, so understanding this relationship will help to refine how physicists and astrophysicists understand it. Euclid's mission advances and complements ESA's Planck telescope, ''Planck'' telescope (2009 to 2013). The mission is named after the ancient Greek mathematician Euclid. Euclid is a medium-class ("M-class") mission and is part of the Cosmic Vision campaign of ESA's European S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Optics
Euclid's ''Optics'' ( grc-gre, Ὀπτικά), is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC. The earliest surviving manuscript of ''Optics'' is in Greek and dates from the 10th century AD. The work deals almost entirely with the geometry of vision, with little reference to either the physical or psychological aspects of sight. No Western scientist had previously given such mathematical attention to vision. Euclid's ''Optics'' influenced the work of later Greek, Islamic, and Western European Renaissance scientists and artists. Historical significance Writers before Euclid had developed theories of vision. However, their works were mostly philosophical in nature and lacked the mathematics that Euclid introduced in his ''Optics''. Efforts by the Greeks prior to Euclid were concerned primarily with the physical dimension of vision. Whereas Plato and Empedocles thought of the visual ray as "luminous and ethereal emanation", Euclidâ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclid's Elements
The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century. Euclid's ''Elements'' has been referred to as the most successful and influential textbook ever written. It was one of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number of editions published since the first printing i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: ''If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.'' This postulate does not specifically talk about parallel lines; it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23 just before the five postulates. ''Euclidean geometry'' is the study of geometry that satisfies all of Euclid's axioms, ''including'' the parallel postulate. The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually, it was discovered that inverting the postulate gave valid, albeit differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Topology
In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n-dimensional Euclidean space \R^n by the Euclidean distance, Euclidean metric. Definition The Euclidean norm on \R^n is the non-negative function \, \cdot\, : \R^n \to \R defined by \left\, \left(p_1, \ldots, p_n\right)\right\, ~:=~ \sqrt. Like all Norm (mathematics), norms, it induces a canonical Metric (mathematics), metric defined by d(p, q) = \, p - q\, . The metric d : \R^n \times \R^n \to \R induced by the Euclidean norm is called the Euclidean metric or the Euclidean distance and the distance between points p = \left(p_1, \ldots, p_n\right) and q = \left(q_1, \ldots, q_n\right) is d(p, q) ~=~ \, p - q\, ~=~ \sqrt. In any metric space, the Ball (mathematics), open balls form a Base (topology), base for a topology on that space.Metric space, Metric space#Open and closed sets.2C topology and convergence The Euclidean topology on \R^n is the topology by these balls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Relation
In mathematics, Euclidean relations are a class of binary relations that formalize " Axiom 1" in Euclid's ''Elements'': "Magnitudes which are equal to the same are equal to each other." Definition A binary relation ''R'' on a set ''X'' is Euclidean (sometimes called right Euclidean) if it satisfies the following: for every ''a'', ''b'', ''c'' in ''X'', if ''a'' is related to ''b'' and ''c'', then ''b'' is related to ''c''.. To write this in predicate logic: :\forall a, b, c\in X\,(a\,R\, b \land a \,R\, c \to b \,R\, c). Dually, a relation ''R'' on ''X'' is left Euclidean if for every ''a'', ''b'', ''c'' in ''X'', if ''b'' is related to ''a'' and ''c'' is related to ''a'', then ''b'' is related to ''c'': :\forall a, b, c\in X\,(b\,R\, a \land c \,R\, a \to b \,R\, c). Properties # Due to the commutativity of ∧ in the definition's antecedent, ''aRb'' ∧ ''aRc'' even implies ''bRc'' ∧ ''cRb'' when ''R'' is right Euclidean. Similarly, ''bRa'' ∧ ''cRa'' implies ''bRc' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Vector
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a '' directed line segment'', or graphically as an arrow connecting an ''initial point'' ''A'' with a ''terminal point'' ''B'', and denoted by \overrightarrow . A vector is what is needed to "carry" the point ''A'' to the point ''B''; the Latin word ''vector'' means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from ''A'' to ''B''. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
