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1 Let us think about Euclidean geometry first.

2 Previously, Euclidean geometry had stated that parallel lines never meet.

3 For example, recall that in Euclidean geometry the sum of the angles of any triangle is always 1800.

4 But a postulate in a Euclidean system must be accepted in order to maintain the integrity of the whole.

5 It is also mathematics, of course, but Euclidean geometry is by no means the only conceivable mathematical geometry.

6 However, certain ideas taken from ordinary Euclidean geometry are very helpful for us.

7 Why do I refer to Euclidean geometry as a physical theory rather than a branch of mathematics?

8 We choose the Euclidean distance as a similarity coefficient.

9 In the case of non - Euclidean geometry he published no definitive work.

10 Some application of the extended Euclidean algorithm are also given.

11 All the process of clustering based on the Euclidean distance among data vectors.

12 He has been using a mathematical technique called the "Euclidean path integral".

13 Euclidean geometry is not only the leader of the civilization of ancient Greek but also the brilliant achievements of axiomatic approach in mathematics.

14 In this paper,(www.Sentencedict.com) empirical euclidean likelihood ratio statistics are constructed for parametric in a nonlinear model. And prove strong consistency and asymptotic normality of the estimation.

15 The euclidean norm of an n - vector x with real or complex components is defined as following.

16 The essential property and developmental course of Euclidean space, symplectic space and bogus space are studied.

17 To avoid the technical difficulties in actually performing the sum over histories, these curved space-times must be taken to be Euclidean.

18 These principles can be applied to energise and bring to life the hard edges of Euclidean geometry and of the drawing board.

19 However, this revelation did not bring about the destruction of Euclidean geometry[Sentencedict.com], it simply added to it.

20 The common conclusion was the uniqueness and necessity of Euclidean geometry.

21 Entering in details of cluster number 41 , Table 5 reports the customer with the largest Euclidean distance from the prototype.

22 The error performance of continuous phase modulation (CPM) with optimal coherent detection depends on the minimum squared Euclidean distance (MSED).

23 The finite temperature and chemical potential axial anomalies in Euclidean space are studied within the framework of Perturbation theory.

24 These observations allow one to formalize the definition of reflection: a reflection is an involutive isometry of an Euclidean space whose set of fixed points is an affine subspace of codimension 1.

25 It was this concept that Riemann generalized, thereby opening up new vistas in non - Euclidean geometry.

26 Lorentzian wormholes are mainly studied in semiclassical gravity and Euclidean wormholes are studied in particle physics.

27 The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.

28 The Lorentz transformation of orthogonal bases is derived by means of matrix Euclidean four dimension space.

29 Numerical results show that there is no matching issue for an OOK system using binary linear block code because its bijection between Hamming distance and Euclidean distance.

30 The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space.