# Dimensional Space

### 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 ...
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 ...
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 ...
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 ...
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 ...

### 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)