How to use Euclidean in a sentence

Looking for sentences and phrases with the word Euclidean? Here are some examples.

Sentence Examples But that law assumes the conservation of mass energy as well as a space which is Euclidean. If physical space and perceptual space are the same thing, then Kant is claiming we know a priori that physical space is Euclidean. It is important to note, however, that the extra dimension, though curled up, was still Euclidean in nature. Not all right triangles constructible in Euclidean geometry can be constructed in Pythagorean geometry. The latter are mediated by DNA-loops bringing two chemically remote segments of the DNA close in Euclidean space. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. Something that exists nowhere and exists along the lines of Euclidean geometry, judging by what I understand of it, cannot exist. See this issue's mystery mix for a comparison of Euclidean, hyperbolic, and spherical geometry. And generally, often in so-called logical thinking, we depend upon using the analogy of Euclidean or Cartesian argument, to define policy. Kaluznin also worked in the area of geometrical algebra, particularly on arrangements of subspaces in Euclidean and unitary spaces. It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well. However he continued to work on topological ideas, in particular embedding complexes in Euclidean space. Squared Euclidean distances were utilized in order to maximize the dissimilarity of unlike clusters. Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of linear and angular momentum. At this time thinking was dominated by Kant who had stated that Euclidean geometry is the inevitable necessity of thought. Euclidean geometry studies Euclidean-space-structure, topology studies topological structures, and so on. What is the expected path length L of the optimum travelling salesman problem tour in Euclidean norm? A method to obtain a good approximation to the trisector of an angle by Euclidean construction is also given. The second chapter presents a development of absolute and Euclidean geometry based on Hilbert's axioms. In this case, one would like good algorithms for embedding specifically into 2-and 3-dimensional Euclidean spaces. Show More Sentences These large matrices describe high-dimensional Euclidean spaces within which biomolecular sequences can be uniquely represented as vectors. One of the first papers which he published after arriving in the United States was on the Euclidean algorithm in principal ideal domains. Obviously, when no obstacles are used, then the matrix represents a Euclidean space with dimensionality equal to two. A Euclidean geometry is based on false assumptions, which are called definitions, axioms, and postulates. It reduced the problem of consistency of the axioms of non-Euclidean geometry to that of the consistency of the axioms of Euclidean geometry. If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them. The falseness of the idea of principle, is typified by a Cartesian or Euclidean geometry. This indicates that a simple Euclidean distance in feature space can be used to quantify the relative similarity between different mutant types. From this point of view, Euclidean geometry is a very favorable place to begin a student's serious mathematical training. This is, of course, how Beltrami first showed that hyperbolic geometry was no less consistent than Euclidean geometry. Mathematics has considered alternatives to Euclidean space since the early nineteenth century. Similarly, an eliminative structuralist account of real analysis and Euclidean geometry requires a background ontology whose cardinality is at least that of the continuum. Now within any bounded region of Euclidean space it can be shown that Cantor's continua coincide with continua in the sense of the modern definition. The Vertical Angles Conflict Activity was designed for students about to embark upon the study of Euclidean geometry with reference to formal definitions and proofs in class. To sum up, I am asserting that Euclidean geometry is the only mathematical subject that is really in a position to provide the grounds for its own axiomatic procedures. The work of Bolyai and Lobachevsky are comparable in that sense, that they both challenge axiomatic assumptions, but their postulates are of Euclidean geometry. Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings. In this particular ground state, the Euclidean point of view, there are no constraints acting on the developable function, and all directions are the same. The Euclidean construction axiom allows for the extraction of all real square roots and thus includes even more constructions than the Pythagorean axiom. The approach that concentrates on non-Euclidean geometry is ideal for students who already have a mastery of Euclidean geometry, but it cannot replace such a mastery. Show More Sentences This is a peer reviewed journal devoted to the Euclidean geometry. Mapping it onto the Earth's surface is far more complex, however, because there may be little relationship between proximity in Euclidean geographic space and positionality. But why does space have to be Euclidean, nice and flat and square. His famous Euclidean algorithm, when applied to a pair of natural numbers, leads in a finite number of steps to their greatest common divisor. Knuth offers as an example the Euclidean algorithm for determining the greatest common divisor of two natural numbers. We may resolve the paradox, say in the Euclidean theory of quantum gravity, but what if the Euclidean theory of quantum gravity doesn't correctly describe our universe. The Intellectual Beast is bottled up in Euclidean Geometry because he has never awakened his Consciousness. In Borken's messily vital urban context of supermarkets, small houses and traffic roundabouts, the bank's simple Euclidean form is a reassuringly calm, rooted presence. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. The Euclidean algorithm is useful for reducing a common fraction to lowest terms. Mandelbrot was frustrated by the inability of Euclidean geometry to measure natural forms like clouds, mountains and trees. Today we call these three geometries Euclidean, hyperbolic, and absolute. This analysis consisted of producing a matrix of squared Euclidean distances based on Census characteristics. The first is a plane, it is the Euclidean Universe which is our intuitive mental picturing. The way Cabri II Plus manages infinity is to draw extensions to the Euclidean plane which serves as the geometric model for the software. Among other things, E is the only one which looks like a projection of a non-Euclidean triangle into Euclidean space. The agglomerative, or grouping, schedule provided by Ward's method indicated a notable flattening of the curve of squared Euclidean distances after the five-cluster solution. Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields. It remains the case that most people are quite skeptical that we will ever make sense of the Euclidean path integral, especially in the semi-classical regime. A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry. Show More Sentences Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate. A dendrogram depicts the distance in Euclidean or geometric space between a set of objects, in this case, problem categories, according to a set of attributes, whether respondents reported experiencing a problem of that type. Thus, for example, the notions of Euclidean geometry are invariant under similarity transformations, those of affine geometry under affine transformations, and those of topology under bicontinuous transformations. If we picture the universe using Euclidean geometry, we can imagine going straight out forever. Besides being translated, a co-ordinate system may also be rotated.2 This signifies analytically: the relations of Euclidean geometry are covariant with respect to linear orthogonal transformations of the co-ordinates. Most such regions are usually two-dimensional Euclidean planes, but one-dimensional and three-dimensional regions are also possible. The researchers employed the Euclidean algorithm, an efficient way to find the greatest common divisor of two integers, to examine those public key numbers. Euclidean geometry provides a good illustration of this. The first possibility gives Euclidean geometry. You don't need to understand Euclidean geometry to work it out. It is rigorous, like Euclidean geometry, yet twisty, like a pretzel. The round torus metric is most easily constructed via its embedding in a Euclidean space of one higher dimension. As he explains on the company's website:I defined weights for each pair of cities as a function of the Euclidean distance between them and the number of friends between them. If space is curved then Euclidean geometry, which is one of many axiomatic systems, does not apply. From data acquired during the 1998 BOOMERANG flight, we were able to determine the age of the universe-about 14 billion years old-and its geometry, which is flat, also called Euclidean. The squared Euclidean distance between each pair of communities in the matrix was calculated based on the normalized values of each of the 23 variables. Selecting the comparison sites and community groupings with the shortest squared Euclidean distances, and refining the selections in light of fieldwork and survey constraints. Ordinary Euclidean geometry is an example of an infinite Affine geometry since the two axioms are valid in the plane. In the theory of curves in Euclidean space, one of the important and interesting problems is the characterization of a regular curve. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space. Show More Sentences It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. From there, Euclidean geometry could be restructured, placing the fifth postulate among the theorems instead. Atomic objects are real-valued vectors in n-dimensional Euclidean space while complex data structures belong to a hierarchy of multivectors. Like I'm a member of a secret priesthood, guardian of mind-bending knowledge beyond Euclidean space. These map the same reality in different ways, like Euclidean geometry and Riemannian geometry. His father taught him drawing and observational techniques from the age of four and Brunel had learned Euclidean geometry by eight. Euclidean plane or spherical geometry ought to be strictly determined in the potential applications. Specifically, 2x2 real matrices R describe either the Minkowskian plane or the Euclidean plane. The topics include surfaces in Euclidean space, separation and orientability, global extrinsic geometry, and the global geometry of curves. At bottom arbitrary, these bent axes and fractured parallelepipeds were not Euclidean proofs but spoofs of them. Locally in the physical 3-dimensional space we approximate curved surface by the Euclidean plane tangent in a given position. The Euclidean norm is most often used in the Lipschitz optimization, but other norms can also be considered. This corresponds to the incircle of a cross-section and can be computed in linear time using the Euclidean distance transform. These coordinates are determined up to a Euclidean transformation by a fundamental element of the theory, the spatial metric, and are hence linked to the metrical structure postulated by the theory. The Euclidean Hubble coefficient is being defined as the space expansion with respect to Euclidean Distances. It is also known as a type of non-Euclidean Geometry, being in many respects similar to Euclidean Geometry. Sometimes it was clearly a Euclidean artefact amid the infinite variety of organic natural forms. To build, by observing the rules of the Euclidean geometry, with the rule and the compass, an unspecified triangle knowing the length of the three interior bisectrices. In taxicab geometry, the perpendicular bisector and the circle are defined in the same way as in Euclidean geometry, but they look quite different. Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space. Show More Sentences And even with respect to Euclidean space, anything beyond three dimensions ceases to be intuitable, though it can be handled quite well with the tools of mathematics. Thereby there are Smarandache multi-space solutions in the Einstein's gravitational equation, particularly, solutions of combinatorially Euclidean spaces. The simplest mathematical spaces are known as Euclidean spaces. In Euclidean geometry, nonintersecting lines are always parallel. The main purpose of the herein study is to provide a method to build galactic density profiles which requires the conversion of light travel distances to Euclidean distances. An early success of the formalist program was Hilbert's formalization of Euclidean geometry, and the related demonstration of the consistency of those axioms. In mathematics, Euclidean geometry used to be taught in something close to its original presentation two thousand years ago as a rational progression of ideas. Examples from Classical Literature This is the Euclidean case, and the assumption that this case holds is the Euclidean parallel axiom. He returned the proof, saying that he could not accept any of it as elucidating the exact area of a circle, or as Euclidean. He constructed every one of his later speeches on the plan of a Euclidean solution. Their own primitive diagrams, like a badly drawn Euclidean problem, satisfy their idea of studies from the life. The Euclidean geometer can take it for granted that the reader understands what a line or plane, a solid or an angle is. The two-dimensional geometries of Riemann and Lobachevski are thus correlated to the Euclidean geometry. He acted as if he had demonstrated a Euclidean proposition flawlessly. In Euclidean geometry there are right angled triangles and equilateral triangles, but in topology all triangles are the same. In elementary geometry, however, the Euclidean idea is still held. That they are compatible with the Euclidean group is easy to see. Find more words! Another word for Opposite of Meaning of Rhymes with Sentences with Find word forms Translate from English Translate to English Words With Friends Scrabble Crossword / Codeword Words starting with Words ending with Words containing exactly Words containing letters Pronounce Find conjugations Find names From Afrikaans From Albanian From Amharic From Arabic From Armenian From Azerbaijani From Basque From Belarusian From Bengali From Bosnian From Bulgarian From Catalan From Cebuano From Chichewa From Chinese From Corsican From Croatian From Czech From Danish From Dutch From Esperanto From Estonian From Farsi From Filipino From Finnish From French From Frisian From Galician From Georgian From German From Greek From Gujarati From Haitian Creole From Hausa From Hebrew From Hindi From Hmong From Hungarian From Icelandic From Igbo From Indonesian From Irish From Italian From Japanese From Javanese From Kannada From Kazakh From Khmer From Korean From Kurdish From Kyrgyz From Lao From Latin From Latvian From Lithuanian From Luxembourgish From Macedonian From Malagasy From Malay From Malayalam From Maltese From Maori From Marathi From Mongolian From Burmese From Nepali From Norwegian From Polish From Portuguese From Punjabi From Romanian From Russian From Samoan From Scots Gaelic From Serbian From Sesotho From Shona From Sinhala From Slovak From Slovenian From Somali From Spanish From Sundanese From Swahili From Swedish From Tajik From Tamil From Telugu From Thai From Turkish From Ukrainian From Urdu From Uzbek From Vietnamese From Welsh From Xhosa From Yiddish From Yoruba From Zulu To Afrikaans To Albanian To Amharic To Arabic To Armenian To Azerbaijani To Basque To Belarusian To Bengali To Bosnian To Bulgarian To Catalan To Cebuano To Chichewa To Chinese To Corsican To Croatian To Czech To Danish To Dutch To Esperanto To Estonian To Farsi To Filipino To Finnish To French To Frisian To Galician To Georgian To German To Greek To Gujarati To Haitian Creole To Hausa To Hebrew To Hindi To Hmong To Hungarian To Icelandic To Igbo To Indonesian To Irish To Italian To Japanese To Javanese To Kannada To Kazakh To Khmer To Korean To Kurdish To Kyrgyz To Lao To Latin To Latvian To Lithuanian To Luxembourgish To Macedonian To Malagasy To Malay To Malayalam To Maltese To Maori To Marathi To Mongolian To Burmese To Nepali To Norwegian To Polish To Portuguese To Punjabi To Romanian To Russian To Samoan To Scots Gaelic To Serbian To Sesotho To Shona To Sinhala To Slovak To Slovenian To Somali To Spanish To Sundanese To Swahili To Swedish To Tajik To Tamil To Telugu To Thai To Turkish To Ukrainian To Urdu To Uzbek To Vietnamese To Welsh To Xhosa To Yiddish To Yoruba To Zulu English French Afrikaans Word Albanian Word Arabic Word Bengali Word Chinese Word Croatian Word Czech Word Danish Word Dutch Word English Word Finnish Word French Word German Word Greek Word Hindi Word Hungarian Word Icelandic Word Indonesian Word Italian Word Japanese Word Korean Word Latin Word Malay Word Malayalam Word Marathi Word Nepali Word Norwegian Word Polish Word Portuguese Word Romanian Word Russian Word Serbian Word Slovak Word Spanish Word Swahili Word Swedish Word Tamil Word Telugu Word Thai Word Turkish Word Ukrainian Word Uzbek Word Vietnamese Word Welsh Word All words 2-letter words 3-letter words 4-letter words 5-letter words 6-letter words 7-letter words 8-letter words 9-letter words 10-letter words 11-letter words 12-letter words 13-letter words 14-letter words Plural of Singular of Past tense of Present tense of Verb for Adjective for Adverb for Noun for Meaning of name Origin of name Names meaning Names starting with Names of origin Euclidean Use * for blank tiles (max 2) Advanced Search Advanced Search Use * for blank spaces Advanced Search Advanced Word Finder Nearby Words euclidean Euclid euchromatin euchromatic euchred euchre eucrites eucryphia eudaemonia eudaemonism eudaimonia Eudaimonia