Some articles on dimensional, space, dimensional space:
Lie Sphere Geometry in Space and Higher Dimensions - General Theory
... Note that Qn is an (n + 1)-dimensional manifold (spheres are parameterized by their center and radius) ... The space of contact elements is a (2n – 1)-dimensional contact manifold Z2n – 1 in terms of the given choice of point spheres, these contact elements correspond to ... The space Z2n – 1 is therefore isomorphic to the projectivized cotangent bundle of the n-sphere ...
... Note that Qn is an (n + 1)-dimensional manifold (spheres are parameterized by their center and radius) ... The space of contact elements is a (2n – 1)-dimensional contact manifold Z2n – 1 in terms of the given choice of point spheres, these contact elements correspond to ... The space Z2n – 1 is therefore isomorphic to the projectivized cotangent bundle of the n-sphere ...
Line Coordinates - Lines in Three-dimensional Space
... Similarly, for two points in three-dimensional space (x1, y1, z1, w1) and (x2, y2, z2, w2), the line containing them is determined by the six determinants This is the basis for a system of ... This system maps the space of lines in three-dimensional space to a projective space of dimension five, but with the additional requirement the space ... More generally, the lines in n-dimensional projective space are determined by a system of n(n − 1)/2 homogeneous coordinates that satisfy a set of (n − 2)(n ...
... Similarly, for two points in three-dimensional space (x1, y1, z1, w1) and (x2, y2, z2, w2), the line containing them is determined by the six determinants This is the basis for a system of ... This system maps the space of lines in three-dimensional space to a projective space of dimension five, but with the additional requirement the space ... More generally, the lines in n-dimensional projective space are determined by a system of n(n − 1)/2 homogeneous coordinates that satisfy a set of (n − 2)(n ...
Flat (geometry)
... In geometry, a flat is a subset of n-dimensional space that is congruent to a Euclidean space of lower dimension ... The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes ... In n-dimensional space, there are flats of every dimension from 0 to n – 1 ...
... In geometry, a flat is a subset of n-dimensional space that is congruent to a Euclidean space of lower dimension ... The flats in two-dimensional space are points and lines, and the flats in three-dimensional space are points, lines, and planes ... In n-dimensional space, there are flats of every dimension from 0 to n – 1 ...
Geometric Calculus - Covariant Derivative
... A sufficiently smooth k-surface in an n-dimensional space is deemed a manifold ... Locally, B acts as a pseudoscalar of the k-dimensional space ... as the geometric derivative is defined over the entire n-dimensional space, we may wish to define an intrinsic derivative, locally defined on the ...
... A sufficiently smooth k-surface in an n-dimensional space is deemed a manifold ... Locally, B acts as a pseudoscalar of the k-dimensional space ... as the geometric derivative is defined over the entire n-dimensional space, we may wish to define an intrinsic derivative, locally defined on the ...
Ludwig Schläfli - Higher Dimensions
... Around 1850 the general concept of Euclidean space hadn't been developed — but linear equations in variables were well-understood ... interpretation analogous to the cartesian coordinates in three-dimensional space ... the study of the linear geometry of -dimensional space ...
... Around 1850 the general concept of Euclidean space hadn't been developed — but linear equations in variables were well-understood ... interpretation analogous to the cartesian coordinates in three-dimensional space ... the study of the linear geometry of -dimensional space ...
Famous quotes containing the words space and/or dimensional:
“Even the most subjected person has moments of rage and resentment so intense that they respond, they act against. There is an inner uprising that leads to rebellion, however short- lived. It may be only momentary but it takes place. That space within oneself where resistance is possible remains.”
—bell hooks (b. c. 1955)
“I don’t see black people as victims even though we are exploited. Victims are flat, one- dimensional characters, someone rolled over by a steamroller so you have a cardboard person. We are far more resilient and more rounded than that. I will go on showing there’s more to us than our being victimized. Victims are dead.”
—Kristin Hunter (b. 1931)
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