How to use euclidean in a sentence

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Sentence Examples In 1903 he published Geometrie der Dynamen which considered euclidean kinematics and the mechanics of rigid bodies. He worked on conjugate functions in multidimensional euclidean space and the theory of functions of a complex variable. This had the remarkable corollary that non-euclidean geometry was consistent if and only if euclidean geometry was consistent. His interest in mathematics was stimulated during his school years in Izmir by a teacher who encouraged him to solve problems in euclidean geometry. One of the first papers which he published after arriving in the United States was on the Euclidean algorithm in principal ideal domains. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. The second chapter presents a development of absolute and Euclidean geometry based on Hilbert's axioms. However he continued to work on topological ideas, in particular embedding complexes in Euclidean space. 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. Squared Euclidean distances were utilized in order to maximize the dissimilarity of unlike clusters. At this time thinking was dominated by Kant who had stated that Euclidean geometry is the inevitable necessity of thought. Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of linear and angular momentum. It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well. 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. See this issue's mystery mix for a comparison of Euclidean, hyperbolic, and spherical geometry. Something that exists nowhere and exists along the lines of Euclidean geometry, judging by what I understand of it, cannot exist. Not all right triangles constructible in Euclidean geometry can be constructed in Pythagorean geometry. Show More Sentences A Euclidean geometry is based on false assumptions, which are called definitions, axioms, and postulates. If all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them. It reduced the problem of consistency of the axioms of non-Euclidean geometry to that of the consistency of the axioms of Euclidean geometry. This is, of course, how Beltrami first showed that hyperbolic geometry was no less consistent than Euclidean geometry. The falseness of the idea of principle, is typified by a Cartesian or Euclidean geometry. From this point of view, Euclidean geometry is a very favorable place to begin a student's serious mathematical training. Mathematics has considered alternatives to Euclidean space since the early nineteenth century. 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. The latter are mediated by DNA-loops bringing two chemically remote segments of the DNA close in Euclidean space. In this case, one would like good algorithms for embedding specifically into 2-and 3-dimensional Euclidean spaces. Obviously, when no obstacles are used, then the matrix represents a Euclidean space with dimensionality equal to two. This indicates that a simple Euclidean distance in feature space can be used to quantify the relative similarity between different mutant types. These large matrices describe high-dimensional Euclidean spaces within which biomolecular sequences can be uniquely represented as vectors. 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. 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. 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. Today we call these three geometries Euclidean, hyperbolic, and absolute. Similarly, an eliminative structuralist account of real analysis and Euclidean geometry requires a background ontology whose cardinality is at least that of the continuum. Show More Sentences 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 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. The work of Bolyai and Lobachevsky are comparable in that sense, that they both challenge axiomatic assumptions, but their postulates are of Euclidean geometry. 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. Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings. 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. The Euclidean construction axiom allows for the extraction of all real square roots and thus includes even more constructions than the Pythagorean axiom. This is a peer reviewed journal devoted to the Euclidean geometry. But why does space have to be Euclidean, nice and flat and square. 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. 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. A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry. 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. 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. Most such regions are usually two-dimensional Euclidean planes, but one-dimensional and three-dimensional regions are also possible. The topics include surfaces in Euclidean space, separation and orientability, global extrinsic geometry, and the global geometry of curves. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space. It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. Locally in the physical 3-dimensional space we approximate curved surface by the Euclidean plane tangent in a given position. Show More Sentences Specifically, 2x2 real matrices R describe either the Minkowskian plane or the Euclidean plane. Like I'm a member of a secret priesthood, guardian of mind-bending knowledge beyond Euclidean space. The round torus metric is most easily constructed via its embedding in a Euclidean space of one higher dimension. In the theory of curves in Euclidean space, one of the important and interesting problems is the characterization of a regular curve. Atomic objects are real-valued vectors in n-dimensional Euclidean space while complex data structures belong to a hierarchy of multivectors. This corresponds to the incircle of a cross-section and can be computed in linear time using the Euclidean distance transform. At bottom arbitrary, these bent axes and fractured parallelepipeds were not Euclidean proofs but spoofs of them. Euclidean plane or spherical geometry ought to be strictly determined in the potential applications. From there, Euclidean geometry could be restructured, placing the fifth postulate among the theorems instead. The Euclidean Hubble coefficient is being defined as the space expansion with respect to Euclidean Distances. His father taught him drawing and observational techniques from the age of four and Brunel had learned Euclidean geometry by eight. Sometimes it was clearly a Euclidean artefact amid the infinite variety of organic natural forms. These map the same reality in different ways, like Euclidean geometry and Riemannian geometry. It is also known as a type of non-Euclidean Geometry, being in many respects similar to Euclidean Geometry. If we picture the universe using Euclidean geometry, we can imagine going straight out forever. If space is curved then Euclidean geometry, which is one of many axiomatic systems, does not apply. Ordinary Euclidean geometry is an example of an infinite Affine geometry since the two axioms are valid in the plane. The Euclidean norm is most often used in the Lipschitz optimization, but other norms can also be considered. In Euclidean geometry, nonintersecting lines are always parallel. The simplest mathematical spaces are known as Euclidean spaces. Show More Sentences An early success of the formalist program was Hilbert's formalization of Euclidean geometry, and the related demonstration of the consistency of those axioms. Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space. 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. In taxicab geometry, the perpendicular bisector and the circle are defined in the same way as in Euclidean geometry, but they look quite different. 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. 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 If we set out to solve a problem by non-euclidean geometry, we don't switch to euclidean postulates. 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. This is the Euclidean case, and the assumption that this case holds is the Euclidean parallel axiom. That they are compatible with the Euclidean group is easy to see. In elementary geometry, however, the Euclidean idea is still held. 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. Find more words! 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