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위키데이터

• ID : Q162886

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1. The modern version of Euclidean geometry is the theory of Euclidean (coordinate) spaces of multiple dimensions, where distance is measured by a suitable generalization of the Pythagorean theorem .
2. Euclidean geometry , the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid (c. 300 bce).
3. In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools.
4. Indeed, until the second half of the 19th century, when non-Euclidean geometries attracted the attention of mathematicians, geometry meant Euclidean geometry.
5. Euclidean Geometry is considered as an axiomatic system, where all the theorems are derived from the small number of simple axioms.
6. Since the term “Geometry” deals with things like points, line, angles, square, triangle, and other shapes, the Euclidean Geometry is also known as the “plane geometry”.
7. He gave five postulates for plane geometry known as Euclid’s Postulates and the geometry is known as Euclidean geometry.
8. Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of simple axioms.
9. Until the advent of non-Euclidean geometry, these axioms were considered to be obviously true in the physical world, so that all the theorems would be equally true.
10. Euclidean geometry also allows the method of superposition, in which a figure is transferred to another point in space.
11. The fundamental types of measurements in Euclidean geometry are distances and angles, both of which can be measured directly by a surveyor.
12. Abstract Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space.
13. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry.
14. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility.
15. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry.
16. He found through his general theory of relativity that a non-Euclidean geometry is not just a possibility that Nature happens not to use.
17. Before the 19 th century only one geometry was studied in any depth or thought to be an accurate or correct description of physical space, and that was Euclidean geometry.
18. Projective geometry can be thought of as a deepening of the non-metrical and formal sides of Euclidean geometry; non-Euclidean geometry as a challenge to its metrical aspects and implications.
19. By the opening years of the 20 th century a variety of Riemannian differential geometries had been proposed, which made rigorous sense of non-Euclidean geometry.
20. Thus, for Locke, Euclidean geometry provided one kind of knowledge, and experience and scientific experiment, another.
21. In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs.
22. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings.
23. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well.
24. The Elements goes on to the solid geometry of three dimensions, and Euclidean geometry was subsequently extended to any finite number of dimensions.
25. It also is no longer taken for granted that Euclidean geometry describes physical space.
26. Following a precedent set in the Elements, Euclidean geometry has been exposited as an axiomatic system, in which all theorems ("true statements") are derived from a finite number of axioms.
27. We now see that Euclidean geometry should be embedded in first-order logic with identity, a formal system first set out in Hilbert and Wilhelm Ackermann's 1928 Principles of Theoretical Logic.
28. This course is designed to support instructors who are teaching elements of Euclidean geometry, from properties of triangles and circles to applications.
29. IT is interesting to compare the attitudes of the two most recent writers in English who deal with Euclidean geometry.
30. Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes.
31. Hyperbolic geometry shares many proofs and theorems with Euclidean geometry, and provides a novel and beautiful prospective from which to view those theorems.
32. The parallel axiom (fifth postulate) occupies a special place in the axiomatics of Euclidean geometry.
33. The first sufficiently precise axiomatization of Euclidean geometry was given by D. Hilbert (see Hilbert system of axioms).
34. Euclidean geometry avoided the use of distance measurements, preferring to consider areas of squares built on segments.
35. This is probably the main reason why we prefer to think of the world around us in terms of Euclidean geometry — this makes calculations easier.
36. Locally, every geometry can be approximated by Euclidean geometry.
37. "Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems.
38. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry.
39. The philosophical importance of non-Euclidean geometry was that it greatly clarified the relationship between mathematics, science and observation.
40. After Einstein, even this belief had to be abandoned, and it is now known that Euclidean geometry is only an approximation to the geometry of actual, physical space.
41. I have recently been studying Euclid (the "father" of geometry), and was amazed to find out about the existence of a non-Euclidean geometry.
42. Being as curious as I am, I would like to know about non-Euclidean geometry.
43. We already have on this web site a detailed description of one kind of non-Euclidean geometry called projective geometry.
44. In Euclidean Geometry, isn't a line means a straight line and a plane means a flat plane?
45. Nikolai I. Lobachevsky was the first to actually publish an account of non-Euclidean geometry in 1829.
46. This unique book overturns our ideas about non-Euclidean geometry and the fine-structure constant, and attempts to solve long-standing mathematical problems.

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위키데이터

• ID : Q162886

Spacy 패턴 목록

• [{'LOWER': 'euclidean'}, {'LEMMA': 'geometry'}]