elliptic geometry sentence in Hindi
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- One way in which elliptic geometry differs from Euclidean geometry is that the sum of the interior angles of a triangle is greater than 180 degrees.
- More generally, the term " motion " is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry.
- Their research uncovered two types of spaces whose geometric structures differ from that of classical Euclidean space; these gave rise to hyperbolic geometry and elliptic geometry.
- Absolute geometry is inconsistent with elliptic geometry : in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist.
- Absolute geometry is inconsistent with elliptic geometry : in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist.
- Spherical geometry is " not " elliptic geometry, but shares with that geometry the property that a line has no parallels through a given point.
- The parallel property of elliptic geometry is the key idea that leads to the principle of projective duality, possibly the most important property that all projective geometries have in common.
- I know that, in elliptic geometry, it's possible to have a triangle with three right angles thus adding up to 270?rather than the Euclidian 180?
- Some say one should face the direction which would be the shortest distance to Jerusalem, i . e . the arc of a great circle, as defined in elliptic geometry.
- This study became widely accessible through the Poincar?disc model where Riemann, a student of Gauss's, constructed Riemannian geometry, of which elliptic geometry is a particular case.
- Absolute geometry is inconsistent with elliptic geometry : in that theory, there are no parallel lines at all, but it is a theorem of absolute geometry that parallel lines do exist.
- One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry ( a fundamental part of astronomy and navigation ).
- In elliptic geometry, an "'elliptic rectangle "'is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90?
- For example, the first and fourth of Euclid's postulates, that there is a unique line between any two points and that all right angles are equal, hold in elliptic geometry.
- Because Euclidean, hyperbolic and elliptic geometry are all consistent, the question arises : which is the real geometry of space, and if it is hyperbolic or elliptic, what is its curvature?
- More precisely, the surface of a sphere is a model of elliptic geometry if lines are modeled by great circles, and points at each other's antipodes are considered to be the same point.
- It was Grossmann who emphasized the importance of a non-Euclidean geometry called Riemannian geometry ( also elliptic geometry ) to Einstein, which was a necessary step in the development of Einstein's general theory of relativity.
- Other metric spaces occur for example in elliptic geometry and hyperbolic geometry, where distance on a sphere measured by angle is a metric, and the hyperboloid model of hyperbolic geometry is used by special relativity as a metric space of velocities.
- Even though elliptic geometry is not an extension of absolute geometry ( as Euclidean and hyperbolic geometry are ), there is a certain " symmetry " in the propositions of the three geometries that reflects a deeper connection which was observed by Felix Klein.
- Geometries that are specializations of real projective geometry, such as Euclidean geometry, elliptic geometry or conformal geometry may be complexified, thus embedding the points of the geometry in a complex projective space, but retaining the identity of the original real space as special.
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