Euclidean Space
المؤلف:
Gray, A.
المصدر:
"Euclidean Spaces." §1.1 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press
الجزء والصفحة:
...
2-8-2021
2171
Euclidean Space
Euclidean 
-space, sometimes called Cartesian space or simply 
-space, is the space of all n-tuples of real numbers, (
, 
, ..., 
). Such 
-tuples are sometimes called points, although other nomenclature may be used (see below). The totality of 
-space is commonly denoted 
, although older literature uses the symbol 
(or actually, its non-doublestruck variant 
; O'Neill 1966, p. 3).
is a vector space and has Lebesgue covering dimension 
. For this reason, elements of 
are sometimes called 
-vectors. 
is the set of real numbers (i.e., the real line), and 
is called the Euclidean plane. In Euclidean space, covariant and contravariant quantities are equivalent so 
.
REFERENCES:
Gray, A. "Euclidean Spaces." §1.1 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 2-5, 1997.
O'Neill, B. Elementary Differential Geometry. San Diego, CA: Academic Press, 1966.
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