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https://en.wikipedia.org/wiki/Jonathan%20Borwein | Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the University of Newcastle, Australia. He was a close associate of David H. Bailey, and they have been prominent public advocates of experimental mathematics.
Borwein's i... |
https://en.wikipedia.org/wiki/Climbing%20Mount%20Improbable | Climbing Mount Improbable is a 1996 popular science book by Richard Dawkins. The book is about probability and how it applies to the theory of evolution. It is designed to debunk claims by creationists about the probability of naturalistic mechanisms like natural selection.
The main metaphorical treatment is of a geog... |
https://en.wikipedia.org/wiki/Pairing%20function | In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number.
Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.
Definition
A pairing function is a bijection
More generally, a ... |
https://en.wikipedia.org/wiki/Lucas%E2%80%93Carmichael%20number | In mathematics, a Lucas–Carmichael number is a positive composite integer n such that
if p is a prime factor of n, then p + 1 is a factor of n + 1;
n is odd and square-free.
The first condition resembles the Korselt's criterion for Carmichael numbers, where -1 is replaced with +1. The second condition eliminates from... |
https://en.wikipedia.org/wiki/GGP | GGP may refer to:
Gan–Gross–Prasad conjecture, a conjecture in number theory
Garden Grove Playhouse, a former theater group in Orange County, California
Gateway-to-Gateway Protocol
General game playing, in artificial intelligence
General Growth Properties, since 2018 part of Brookfield Properties
Generations and ... |
https://en.wikipedia.org/wiki/Kac%E2%80%93Moody%20algebra | In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-di... |
https://en.wikipedia.org/wiki/Current%20algebra | Certain commutation relations among the current density operators in quantum field theories define an infinite-dimensional Lie algebra called a current algebra. Mathematically these are Lie algebras consisting of smooth maps from a manifold into a finite dimensional Lie algebra.
History
The original current algebra, p... |
https://en.wikipedia.org/wiki/Cartan%20matrix | In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices in the context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is due to Cartan.
Lie algebras
A (symmetrizable) generalize... |
https://en.wikipedia.org/wiki/Whitney%20immersion%20theorem | In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for , any smooth -dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean -space, and a (not necessarily one-to-one) immersion in -space. Similarly, every smooth -d... |
https://en.wikipedia.org/wiki/Buddhabrot | The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. Its name reflects its pareidolic resemblance to classical depictions of Gautama Buddha, seated in a meditation pose with a forehead mark (tikka), a traditional oval crown (ushnisha), and ringlet of hair.
... |
https://en.wikipedia.org/wiki/Net%20%28polyhedron%29 | In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to b... |
https://en.wikipedia.org/wiki/John%20Britton%20%28mathematician%29 | John Leslie Britton (18 November 1927 – 13 June 1994) was an English mathematician from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical Society and was Secretary of Meetings and Membership with that organization from 19... |
https://en.wikipedia.org/wiki/Ranked%20list%20of%20Paraguayan%20departments | Population figures from the 2021 statistics by the INE, the National Statistics Institute.
By population
By area
By density
This is a list of regions of Paraguay by Human Development Index as of 2017.
References
Paraguay
Human Development Index
List
departments |
https://en.wikipedia.org/wiki/1591%20in%20science | The year 1591 in science and technology included many events, some of which are listed here.
Mathematics
François Viète publishes In Artem Analyticien Isagoge, introducing the new algebra with innovative use of letters as parameters in equations.
Giordano Bruno publishes and in Francfort.
Technology
The Rialto B... |
https://en.wikipedia.org/wiki/ALGO | ALGO is an algebraic programming language developed for the Bendix G-15 computer.
ALGO was one of several programming languages inspired by the Preliminary Report on the International Algorithmic Language written in Zürich in 1958. This report underwent several modifications before becoming the Revised Report on which... |
https://en.wikipedia.org/wiki/Antonio%20Abetti | Antonio Abetti (19 June 1846 – 20 February 1928) was an Italian astronomer.
Born in San Pietro di Gorizia (Šempeter-Vrtojba), he earned a degree in mathematics and engineering at the University of Padua. He was married to Giovanna Colbachini in 1879 and they had two sons. He died in Arcetri.
Work
Abetti mainly worke... |
https://en.wikipedia.org/wiki/157%20%28number%29 | 157 (one hundred [and] fifty-seven) is the number following 156 and preceding 158.
In mathematics
157 is:
the 37th prime number. The next prime is 163 and the previous prime is 151.
a balanced prime, because the arithmetic mean of those primes yields 157.
an emirp.
a Chen prime.
the largest known prime p which ... |
https://en.wikipedia.org/wiki/Power%20series%20solution%20of%20differential%20equations | In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
Method
Cons... |
https://en.wikipedia.org/wiki/Thue%20equation | In mathematics, a Thue equation is a Diophantine equation of the form
ƒ(x,y) = r,
where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue, who in 1909 proved that a Thue equation can have only finitely many solutions in i... |
https://en.wikipedia.org/wiki/BRL-CAD | BRL-CAD is a constructive solid geometry (CSG) solid modeling computer-aided design (CAD) system. It includes an interactive geometry editor, ray tracing support for graphics rendering and geometric analysis, computer network distributed framebuffer support, scripting, image-processing and signal-processing tools. The ... |
https://en.wikipedia.org/wiki/Steiner%20point | A Steiner point (named after Jakob Steiner) may refer to:
Steiner point (computational geometry), a point added in solving a geometric optimization problem to make its solution better
Steiner point (triangle), a certain point on the circumcircle of a given triangle
One of 20 points associated with a given set of six po... |
https://en.wikipedia.org/wiki/Mathematics%20Genealogy%20Project | The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians. it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title (in its Mathemat... |
https://en.wikipedia.org/wiki/Signature%20%28topology%29 | In the field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension divisible by four.
This invariant of a manifold has been studied in detail, starting with Rokhlin's theorem for 4-manifolds, and Hirzebruch signature theorem.
Definition
Given a connected and ori... |
https://en.wikipedia.org/wiki/Capitulation | Capitulation may have the following special meanings.
Capitulation (surrender)
Stock market capitulation
Capitulation (treaty)
Capitulations of the Ottoman Empire
Capitulation (algebra)
Conclave capitulation
Electoral capitulation |
https://en.wikipedia.org/wiki/William%20Smith%20%28teacher%29 | William Macdonald Smith (born 25 June 1939) is a South African science and mathematics teacher who is best known for his maths and science lessons on television. Born in Makhanda (Grahamstown), he is the son of the ichthyologist Margaret Mary Smith and Professor J. L. B. Smith, the renowned chemist and ichthyologist wh... |
https://en.wikipedia.org/wiki/Karl%20Adams%20%28mathematician%29 | Karl Adams (1811 in Merscheid – 14 November 1849, in Winterthur) was a Swiss mathematician and teacher who specialised in synthetic geometry.
Publications
Lehre von den Transversalen, 1843
Die harmonischen Verhältnisse, 1845
Die merkwürdigen Eigenschaften des geradlinigen Dreiecks, 1846
Das Malfattische Problem, 1... |
https://en.wikipedia.org/wiki/Darboux%20vector | In differential geometry, especially the theory of space curves, the Darboux vector is the angular velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it. It is also called angular momentum vector, because it is directly proportional to angular momentum.
In terms of ... |
https://en.wikipedia.org/wiki/Graded%20vector%20space | In mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers.
For "pure" vector spaces, the concept has been introduced in homological algebra, and it... |
https://en.wikipedia.org/wiki/Doubling | Doubling may refer to:
Mathematics
Arithmetical doubling of a count or a measure, expressed as:
Multiplication by 2
Increase by 100%, i.e. one-hundred percent
Doubling the cube (i. e., hypothetical geometric construction of a cube with twice the volume of a given cube)
Doubling time, the length of time required... |
https://en.wikipedia.org/wiki/Helmholtz%20equation | In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation
where is the Laplace operator, is the eigenvalue, and is the (eigen)function. When the equation is applied to waves, is known as the wave number. The Helmholtz equat... |
https://en.wikipedia.org/wiki/Heinrich%20Heesch | Heinrich Heesch (June 25, 1906 – July 26, 1995) was a German mathematician. He was born in Kiel and died in Hanover.
In Göttingen he worked on Group theory. In 1933 Heesch witnessed the National Socialist purges of university staff. Not willing to become a member of the National Socialist organization of university te... |
https://en.wikipedia.org/wiki/Nilakantha%20Somayaji | Keļallur Nilakantha Somayaji (14 June 1444 – 1545), also referred to as Keļallur Comatiri, was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an e... |
https://en.wikipedia.org/wiki/Narayana%20Pandita%20%28mathematician%29 | Nārāyaṇa Paṇḍita () (1340–1400) was an Indian mathematician. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school. He wrote the Ganita Kaumudi (lit "Moonlight of mathematics") in 1356 about mathematical operations. The work antic... |
https://en.wikipedia.org/wiki/Transcendental%20number%20theory | Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.
Transcendence
The fundamental theorem of algebra tells us that if we have a non-constant... |
https://en.wikipedia.org/wiki/Hasse%E2%80%93Weil%20zeta%20function | In mathematics, the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex plane defined in terms of the number of points on the variety after reducing modulo each prime number p. It is a global L-function defined as an Euler product... |
https://en.wikipedia.org/wiki/List%20of%20Indian%20mathematicians | The chronology of Indian mathematicians spans from the Indus Valley civilisation and the Vedas to Modern India.
Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. Hindu-Arabic numerals predominantly used today and... |
https://en.wikipedia.org/wiki/Virahanka | Virahanka (Devanagari: विरहाङ्क) was an Indian prosodist who is also known for his work on mathematics. He may have lived in the 6th century, but it is also possible that he worked as late as the 8th century.
His work on prosody builds on the Chhanda-sutras of Pingala (4th century BCE), and was the basis for a 12th-c... |
https://en.wikipedia.org/wiki/Parameshvara%20Nambudiri | Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of observational astronomy in medieval India and he himself had made a series of ec... |
https://en.wikipedia.org/wiki/Baudhayana%20sutras | The (Sanskrit: बौधायन) are a group of Vedic Sanskrit texts which cover dharma, daily ritual, mathematics and is one of the oldest Dharma-related texts of Hinduism that have survived into the modern age from the 1st-millennium BCE. They belong to the Taittiriya branch of the Krishna Yajurveda school and are among the... |
https://en.wikipedia.org/wiki/Farkas%20Bolyai | Farkas Bolyai (; 9 February 1775 – 20 November 1856; also known as Wolfgang Bolyai in Germany) was a Hungarian mathematician, mainly known for his work in geometry.
Biography
Bolyai was born in Bolya, a village near Hermannstadt, Grand Principality of Transylvania (now Buia, Sibiu County, Romania). His father was Gásp... |
https://en.wikipedia.org/wiki/Chartered%20Mathematician | Chartered Mathematician (CMath) is a professional qualification in Mathematics awarded to professional practising mathematicians by the Institute of Mathematics and its Applications (IMA) in the United Kingdom.
Chartered Mathematician is the IMA's highest professional qualification; achieving it is done through a rigo... |
https://en.wikipedia.org/wiki/ProBoards | ProBoards is a free, remotely hosted message board service that facilitates online discussions by allowing people to create their own online communities.
Ownership and service statistics
ProBoards was founded by Patrick Clinger, who wrote the ProBoards software. Prior to launching ProBoards, Clinger had run HostedScri... |
https://en.wikipedia.org/wiki/Raj%20Chandra%20Bose | Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him. He also invented the notions of partial geometry... |
https://en.wikipedia.org/wiki/A.%20A.%20Krishnaswami%20Ayyangar | A. A. Krishnaswami Ayyangar (1892–1953) was an Indian mathematician. He received his M.A. in Mathematics at the age of 18 from Pachaiyappa's College, and subsequently taught mathematics there. In 1918, he joined the mathematics department of the University of Mysore and retired from there in 1947. He was born in a Tami... |
https://en.wikipedia.org/wiki/Vijay%20Kumar%20Patodi | Vijay Kumar Patodi (12 March 1945 – 21 December 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the index theorem for elliptic operators. He was a professor at Tata Institute of Fun... |
https://en.wikipedia.org/wiki/Knot%20group | In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,
Other conventions consider knots to be embedded in the 3-sphere, in which case the knot group is the fundamental group of its compleme... |
https://en.wikipedia.org/wiki/ISTAT | ISTAT may refer to:
International Society of Transport Aircraft Trading
National Institute of Statistics (Italy) or Istituto Nazionale di Statistica
i-STAT, a blood analyzer made by Abbott Laboratories |
https://en.wikipedia.org/wiki/David%20J.%20Simms | David John Simms (13 January 1933 – 24 June 2018) was an Indian-born Irish mathematician who was a Fellow Emeritus and former Associate Professor of Mathematics at Trinity College, Dublin. Born in Sankeshwar, Mysore (the state now known as Karnataka), India, he specialized in differential geometry and geometric quantis... |
https://en.wikipedia.org/wiki/Principle%20of%20distributivity | The principle of distributivity states that the algebraic distributive law is valid, where both logical conjunction and logical disjunction are distributive over each other so that for any propositions A, B and C the equivalences
and
hold.
The principle of distributivity is valid in classical logic, but both valid a... |
https://en.wikipedia.org/wiki/Is%20Logic%20Empirical%3F | "Is Logic Empirical?" is the title of two articles (one by Hilary Putnam and another by Michael Dummett) that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide groun... |
https://en.wikipedia.org/wiki/Exponential%20formula | In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.
The exponential formula is a power-series version of a special... |
https://en.wikipedia.org/wiki/Magnetic%20reconnection | Magnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave s... |
https://en.wikipedia.org/wiki/Reflexivity | Reflexivity might mean:
Reflexivity (grammar)
Reflexivity (social theory)
Self-reflexivity (see Self-reference)
See also
Reflectivism
Reflexive (disambiguation)
Reflexive operator algebra
Reflexive pronoun
Reflexive relation
Reflexive space
Reflexive verb
Sesquilinear form |
https://en.wikipedia.org/wiki/Assist%20%28association%20football%29 | In association football, an assist is a contribution by a player which helps to score a goal. Statistics for assists made by players may be kept officially by the organisers of a competition, or unofficially by, for example, journalists or organisers of fantasy football competitions. Recording assists is not part of th... |
https://en.wikipedia.org/wiki/Nilpotent%20matrix | In linear algebra, a nilpotent matrix is a square matrix N such that
for some positive integer . The smallest such is called the index of , sometimes the degree of .
More generally, a nilpotent transformation is a linear transformation of a vector space such that for some positive integer (and thus, for all ). ... |
https://en.wikipedia.org/wiki/List%20of%20mathematical%20knots%20and%20links | This article contains a list of mathematical knots and links. See also list of knots, list of geometric topology topics.
Knots
Prime knots
01 knot/Unknot - a simple un-knotted closed loop
31 knot/Trefoil knot - (2,3)-torus knot, the two loose ends of a common overhand knot joined together
41 knot/Figure-eight knot (... |
https://en.wikipedia.org/wiki/Pl%C3%BCcker%20coordinates | In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, . Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in and points on a q... |
https://en.wikipedia.org/wiki/List%20of%20algebraic%20number%20theory%20topics | This is a list of algebraic number theory topics.
Basic topics
These topics are basic to the field, either as prototypical examples, or as basic objects of study.
Algebraic number field
Gaussian integer, Gaussian rational
Quadratic field
Cyclotomic field
Cubic field
Biquadratic field
Quadratic reciprocity
Ideal class ... |
https://en.wikipedia.org/wiki/Toroidal | Toroidal describes something which resembles or relates to a torus or toroid:
Mathematics
Torus
Toroid, a surface of revolution which resembles a torus
Toroidal polyhedron
Toroidal coordinates, a three-dimensional orthogonal coordinate system
Toroidal and poloidal coordinates, directions relative to a torus of referen... |
https://en.wikipedia.org/wiki/Adelic%20algebraic%20group | In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only in case G is a linear algebraic group. ... |
https://en.wikipedia.org/wiki/Tamagawa%20number | In mathematics, the Tamagawa number of a semisimple algebraic group defined over a global field is the measure of , where is the adele ring of . Tamagawa numbers were introduced by , and named after him by .
Tsuneo Tamagawa's observation was that, starting from an invariant differential form ω on , defined over , t... |
https://en.wikipedia.org/wiki/Zero%20matrix | In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of matrices, and is denoted by the symbol or followed by subscripts corresponding to the dimension of the matrix as the context sees fit. ... |
https://en.wikipedia.org/wiki/Markov%20blanket | In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a Markov blanket. If a Markov blanket is minimal, meaning that it cannot drop any variable ... |
https://en.wikipedia.org/wiki/Causal%20Markov%20condition | The Markov condition, sometimes called the Markov assumption, is an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendants, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it.... |
https://en.wikipedia.org/wiki/Chirality%20%28mathematics%29 | In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be achiral.
A chiral object and its mirror image are said to be enantiomor... |
https://en.wikipedia.org/wiki/Disphenocingulum | In geometry, the disphenocingulum or pentakis elongated gyrobifastigium is one of the Johnson solids (). It is one of the elementary Johnson solids that do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.
Cartesian coordinates
Let a ≈ 0.76713 be the second smallest positive root of... |
https://en.wikipedia.org/wiki/Bilunabirotunda | In geometry, the bilunabirotunda is one of the Johnson solids ().
Geometry
It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids.
However, it does have a strong relationship to the icosidodecahedron, an Archimedean solid. Either one of... |
https://en.wikipedia.org/wiki/Triangular%20hebesphenorotunda | In geometry, the triangular hebesphenorotunda is one of the Johnson solids ().
It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. However, it does have a strong relationship to the icosidodecahedron, an Archimedean solid. Most evide... |
https://en.wikipedia.org/wiki/FOCAL%20%28programming%20language%29 | FOCAL (acronym for Formulating On-line Calculations in Algebraic Language, or FOrmula CALculator) is an interactive interpreted programming language based on JOSS and mostly used on Digital Equipment Corporation (DEC) Programmed Data Processor (PDP) series machines.
JOSS was designed to be a simple interactive languag... |
https://en.wikipedia.org/wiki/Augmented%20sphenocorona | In geometry, the augmented sphenocorona is one of the Johnson solids (), and is obtained by adding a square pyramid to one of the square faces of the sphenocorona. It is the only Johnson solid arising from "cut and paste" manipulations where the components are not all prisms, antiprisms or sections of Platonic or Archi... |
https://en.wikipedia.org/wiki/Pasch%27s%20theorem | In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from Euclid's postulates.
Statement
The statement is as follows: [Here, for example, (, , ) means that point lies between points and .]
See also
Ordered geometry
Pasch's axi... |
https://en.wikipedia.org/wiki/Geom | Geom may refer to:
Geom, a Korean sword
GEOM, a modular disk framework used in FreeBSD 5.0 and newer
An abbreviation of geometry
The God-Emperor of Mankind, a core character in the Warhammer 40,000 fictional universe |
https://en.wikipedia.org/wiki/Hendecagram | In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices.
The name hendecagram combines a Greek numeral prefix, hendeca-, with the Greek suffix -gram. The hendeca- prefix derives from Greek ἕνδεκα (ἕν + δέκα, one + ten) meaning "eleven". The -gram suffix derives from γραμμῆ... |
https://en.wikipedia.org/wiki/Jessica%20Utts | Jessica Utts (born 1952) is a parapsychologist and statistics professor at the University of California, Irvine. She is known for her textbooks on statistics and her investigation into remote viewing.
Statistics education
In 2003, Utts published an article in American Statistician, a journal published by the American... |
https://en.wikipedia.org/wiki/Mathematics%20of%20three-phase%20electric%20power | In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y) (also denoted as wye in some areas, as symbolically it is similar to the letter 'Y'... |
https://en.wikipedia.org/wiki/Greenway%20footpath%2C%20London | {
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-0.024483203887939457,
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-0.021221637725830078,
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https://en.wikipedia.org/wiki/Elongated%20triangular%20pyramid | In geometry, the elongated triangular pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a tetrahedron by attaching a triangular prism to its base. Like any elongated pyramid, the resulting solid is topologically (but not geometrically) self-dual.
Formulae
The following... |
https://en.wikipedia.org/wiki/Elongated%20square%20pyramid | In geometry, the elongated square pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a square pyramid () by attaching a cube to its square base. Like any elongated pyramid, it is topologically (but not geometrically) self-dual.
Formulae
The following formulae for the h... |
https://en.wikipedia.org/wiki/Elongated%20triangular%20bipyramid | In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism is one of the Johnson solids (), convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid () by inserting a triangular prism between its congruent halves.... |
https://en.wikipedia.org/wiki/Elongated%20square%20bipyramid | In geometry, the elongated square bipyramid (or elongated octahedron) is one of the Johnson solids (). As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves.
It has been named the pencil cube or 12-faced pencil cube due to its shape.
A zircon crystal ... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20bipyramid | In geometry, the elongated pentagonal bipyramid or pentakis pentagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal bipyramid () by inserting a pentagonal prism between its congruent halves.
Dual polyhedron
The dual of the elongated square bipyramid is... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20cupola | In geometry, the elongated pentagonal cupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal cupola () by attaching a decagonal prism to its base. The solid can also be seen as an elongated pentagonal orthobicupola () with its "lid" (another pentagonal cupola) rem... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20cupola | In geometry, the gyroelongated pentagonal cupola is one of the Johnson solids (J24). As the name suggests, it can be constructed by gyroelongating a pentagonal cupola (J5) by attaching a decagonal antiprism to its base. It can also be seen as a gyroelongated pentagonal bicupola (J46) with one pentagonal cupola removed.... |
https://en.wikipedia.org/wiki/Gyrobifastigium | In geometry, the gyrobifastigium is the 26th Johnson solid (). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is the only Johnson solid that can tile three-dimensional space.
It is also the vertex figure of the nonuniform du... |
https://en.wikipedia.org/wiki/Pentagonal%20orthobicupola | In geometry, the pentagonal orthobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by joining two pentagonal cupolae () along their decagonal bases, matching like faces. A 36-degree rotation of one cupola before the joining yields a pentagonal gyrobicupola ().
The pentagonal orthobi... |
https://en.wikipedia.org/wiki/Pentagonal%20gyrobicupola | In geometry, the pentagonal gyrobicupola is one of the Johnson solids (). Like the pentagonal orthobicupola (), it can be obtained by joining two pentagonal cupolae () along their bases. The difference is that in this solid, the two halves are rotated 36 degrees with respect to one another.
The pentagonal gyrobicupola... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20orthobicupola | In geometry, the elongated pentagonal orthobicupola or cantellated pentagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal orthobicupola () by inserting a decagonal prism between its two congruent halves. Rotating one of the cupolae through 36 degrees bef... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20gyrobicupola | In geometry, the elongated pentagonal gyrobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal gyrobicupola () by inserting a decagonal prism between its congruent halves. Rotating one of the pentagonal cupolae () through 36 degrees before inserting the prism ... |
https://en.wikipedia.org/wiki/Augmented%20triangular%20prism | In geometry, the augmented triangular prism is one of the Johnson solids (). As the name suggests, it can be constructed by augmenting a triangular prism by attaching a square pyramid () to one of its equatorial faces. The resulting solid bears a superficial resemblance to the gyrobifastigium (), the difference being t... |
https://en.wikipedia.org/wiki/Biaugmented%20triangular%20prism | In geometry, the biaugmented triangular prism is one of the Johnson solids (). As the name suggests, it can be constructed by augmenting a triangular prism by attaching square pyramids () to two of its equatorial faces.
It is related to the augmented triangular prism () and the triaugmented triangular prism ().
Exter... |
https://en.wikipedia.org/wiki/Augmented%20pentagonal%20prism | In geometry, the augmented pentagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by augmenting a pentagonal prism by attaching a square pyramid () to one of its equatorial faces.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Biaugmented%20pentagonal%20prism | In geometry, the biaugmented pentagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by doubly augmenting a pentagonal prism by attaching square pyramids () to two of its nonadjacent equatorial faces. (The solid obtained by attaching pyramids to adjacent equatorial faces is not con... |
https://en.wikipedia.org/wiki/Augmented%20hexagonal%20prism | In geometry, the augmented hexagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by augmenting a hexagonal prism by attaching a square pyramid () to one of its equatorial faces. When two or three such pyramids are attached, the result may be a parabiaugmented hexagonal prism (), a... |
https://en.wikipedia.org/wiki/Parabiaugmented%20hexagonal%20prism | In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids () to two of its nonadjacent, parallel (opposite) equatorial faces. Attaching the pyramids to nonadjacent, nonparallel equator... |
https://en.wikipedia.org/wiki/Metabiaugmented%20hexagonal%20prism | In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by doubly augmenting a hexagonal prism by attaching square pyramids () to two of its nonadjacent, nonparallel equatorial faces. Attaching the pyramids to opposite equatorial faces yields a parab... |
https://en.wikipedia.org/wiki/Triaugmented%20hexagonal%20prism | In geometry, the triaugmented hexagonal prism is one of the Johnson solids (). As the name suggests, it can be constructed by triply augmenting a hexagonal prism by attaching square pyramids () to three of its nonadjacent equatorial faces.
See also
Hexagonal prism
References
External links
Johnson solids |
https://en.wikipedia.org/wiki/Augmented%20dodecahedron | In geometry, the augmented dodecahedron is one of the Johnson solids (), consisting of a dodecahedron with a pentagonal pyramid () attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron (), a metabiaugmented dodecahedron (), or a triaugmented dodecah... |
https://en.wikipedia.org/wiki/Parabiaugmented%20dodecahedron | In geometry, the parabiaugmented dodecahedron is one of the Johnson solids (). It can be seen as a dodecahedron with two pentagonal pyramids () attached to opposite faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (), a metabiaugmented dodecahedron (), a tr... |
https://en.wikipedia.org/wiki/Metabiaugmented%20dodecahedron | In geometry, the metabiaugmented dodecahedron is one of the Johnson solids (). It can be viewed as a dodecahedron with two pentagonal pyramids () attached to two faces that are separated by one face. (The two faces are not opposite, but not adjacent either.) When pyramids are attached to a dodecahedron in other ways, t... |
https://en.wikipedia.org/wiki/Triaugmented%20dodecahedron | In geometry, the triaugmented dodecahedron is one of the Johnson solids (). It can be seen as a dodecahedron with three pentagonal pyramids () attached to nonadjacent faces. When pyramids are attached to a dodecahedron in other ways, they may result in an augmented dodecahedron (), a parabiaugmented dodecahedron (), a ... |
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