Flat space

Also found in: Thesaurus, Medical, Encyclopedia, Wikipedia.
(Geom.) See Euclidian space.
- Knight.

See also: Flat

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
Mentioned in ?
References in classic literature ?
One after another they came out on the flat space at the top and stood overcome with wonder.
The houses are irregularly scattered over a flat space of ground, which is cultivated with sweet potatoes and bananas.
They had a flat space before them, on which they alternately threw little square pieces of bone, and were so intent upon their occupation that they never raised eye as he approached them.
One morning, early, we crossed the bar, and while the sun was rising splendidly over the flat spaces of the land we steamed up the innumerable bends, passed under the shadow of the great gilt pagoda, and reached the outskirts of the town.
Let us assume that we have a particle moving freely in a flat space. We denote its contravariant momentum by ([P.sub.0] = [E.sub.0]/c ;P) and the corresponding covariant momentum by ([P.sub.0] - P), such that [P.sup.2.sub.0] - [P.sup.2] = [m.sup.2][c.sup.2], where [E.sub.0] is the energy of the particle, and [P.sub.0], P are constant.
The little remaining flat space hosts plants and rocks--both real and manmade.
Crothers, doesn't eliminate the line-element of the classical "black hole solution" produced by the founders of the problem, but represents the gravitational collapse condition in terms of physical observable quantities accessible to a real observer whose location is in the real Schwazschild space itself, not with the quantities in an abstract flat space tangential to it at the point of observation (as it was in the classical solution).
TC: One of the paintings from this period that riveted my attention bears the Inscription "Here I give thanks to Mondrian." The rectangular form Is embedded In a relatively flat space, very shallow and planar, done In that glossy enamel.
With flat space at a premium on this hillside lot, the parking area outside the front door seemed like a waste of usable space.
[1] makes sense within the context in which we first consider flat space in which we choose a constant frame field, i.e., constant basis polyvectors.
The notion of an expanding universe is based on an unverified assumption that a local distance in a physical space is similar to that of a mathematical Riemannian space embedded in a higher dimensional flat space, and thus the physical meaning of coordinates would necessarily depend on the metric.
We introduce a such point of outlook in an Euclidean flat space, which is tangential to our's in that world-point, where the observer is located.