Some articles on dimensional space, space, dimensional:
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 homogeneous line ... 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 of ... 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 homogeneous line ... 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 of ... 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 ...
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 ... derivative is defined over the entire n-dimensional space, we may wish to define an intrinsic derivative, locally defined on the manifold If a is a vector tangent to the manifold ...
... 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 ... derivative is defined over the entire n-dimensional space, we may wish to define an intrinsic derivative, locally defined on the manifold If a is a vector tangent to the manifold ...
Lie Sphere Geometry in Space and Higher Dimensions - General Theory
... The quadric parameterizes oriented (n – 1)-spheres in n-dimensional space, including hyperplanes and point spheres as limiting cases ... 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 pairs ...
... The quadric parameterizes oriented (n – 1)-spheres in n-dimensional space, including hyperplanes and point spheres as limiting cases ... 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 pairs ...
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 ...
Ludwig Schläfli - Higher Dimensions
... Around 1850 the general concept of Euclidean space hadn't been developed — but linear equations in variables were well-understood ... an interpretation analogous to the cartesian coordinates in three-dimensional space ... which he initiated 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 ... an interpretation analogous to the cartesian coordinates in three-dimensional space ... which he initiated the study of the linear geometry of -dimensional space ...
Famous quotes containing the words space and/or dimensional:
“The within, all that inner space one never sees, the brain and the heart and other caverns where thought and feeling dance their sabbath.”
—Samuel Beckett (1906–1989)
“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)