An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 6 Search : Euclidean
Euclidean
  اقلیدوسی   
Oqlidosi (#)

Fr.: euclidien   

Of or pertaining to Euclid, or his postulates. → Euclidean division, → Euclidean geometry, → Euclidean space, → non-Euclidean geometry.

After the Gk. geometrician and educator at Alexandria, around 300 B.C., who applied the deductive principles of logic to geometry, thereby deriving statements from clearly defined axioms.

Euclidean division
  بخش ِ اقلیدوسی   
baxš-e Oqlidosi

Fr.: division euclidienne   

In arithmetic, the conventional process of division of two → integers. For a → real number a divided by b > 0, there exists a unique integer q and a real number r, 0 ≤ r <b, such that a = qb + r.

Euclidean; → division.

Euclidean geometry
  هندسه‌ی ِ اقلیدوسی   
hendese-ye Oqlidosi (#)

Fr.: géométrie euclidienne   

The geometry based on the postulates or descriptions of Euclid. One of the critical assumptions of the Euclidean geometry is given in his fifth postulate: through a point not on a line, one and only one line be drawn parallel to the given line. See also → non-Euclidean geometry.

Euclidean; → geometry.

Euclidean space
  فضای ِ اقلیدوسی   
fazâ-ye Oqlidosi

Fr.: espace euclidean   

A space in which the → distance between any two points is given by the → Pythagorean theorem: d2 = (Δx)2 + (Δy)2 + (Δz)2, where d is distance and Δx, Δy, and Δz are differential → Cartesian coordinates. Euclidean n-space Rn is the set of all column vectors with n real entries.

Euclidean; → space.

non-Euclidean geometry
  هندسه‌ی ِ نا-اقلیدوسی   
hendese-ye nâ-oqlidosi (#)

Fr.: géométrie non-euclidienne   

Any of several geometries which do not follow the postulates and results of Euclidean geometry. For example, in a non-Euclidean geometry through a point several lines can be drawn parallel to another line. Or, the sum of the interior angles of a triangle differs from 180 degrees. According to Einstein's general relativity theory, gravity distorts space into a non-Euclidean geometry.

non-; → Euclidean geometry.

pseudo-Euclidean space
  فضای ِ دروژ-اقلیدوسی   
fazâ-ye doruž-Oqlidosi

Fr.: espace pseudo-euclidien   

A real vector space of dimension n having a symmetric bilinear form (x, y) such that in some basis e1, ..., en, the quadratic form (x2) takes the form x12 + ... + xn - 12 - xn2. Such bases are called orthonormal.

pseudo-; → Euclidean; → space.