what does this mean?!
and Has any one heared about 2-d matter?
SOURCE OF DEFINITION~Merriam Webster dictionary online*(AOL)
Main Entry: di·men·sion
Pronunciation: d&-'men(t)-sh&n also dI-
Etymology: Middle English, from Middle French, from Latin dimension-, dimensio, from dimetiri to measure out, from dis- + metiri to measure —more at MEASURE
Date: 14th century
1 a (1) : measure in one direction; specifically : one of three coordinates determining a position in space or four coordinates determining a position in space and time (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usually mathematical entities (as an aggregate of points in real or abstract space) <the surface of a sphere has two dimensions>; also : a parameter or coordinate variable assigned to such a property <the three dimensions of momentum> (3) : the number of elements in a basis of a vector space b : the quality of spatial extension : MAGNITUDE, SIZE c : a lifelike or realistic quality d : the range over which or the degree to which something extends : SCOPE — usually used in plural e : one of the elements or factors making up a complete personality or entity : ASPECT
2 : obsolete : bodily form or proportions
3 : any of the fundamental units (as of mass, length, or time) on which a derived unit is based; also : the power of such a unit
4 : wood or stone cut to pieces of specified size
5 : a level of existence or consciousness
- di·men·sion·al /-'mench-n&l, -'men(t)-sh&-n&l/ adjective
- di·men·sion·al·i·ty /-"men(t)-sh&-'na-l&-tE/ noun
- di·men·sion·al·ly /-'mench-n&-lE, -'men(t)-sh&-
(1) See Mariko's post, especially 1a and 3, which are the contexts in which physicists use the term dimension.
(2) Perhaps you are thinking about 2-d systems, which crop up in condensed matter physics a lot? For example, you can have a 2-d lattice of atoms in a material such that that the electrons living on this lattice effectively live in this 2-d sheet. (That's a really rough way of thinking about it.) Note that the 'matter' itself is not two dimensional--atoms have definite volume in 3-space, it's just that the extension in the third dimension is pretty small causing the system to behave in a way where there are only 2 relevant directions.
Dimension has a large number of closely related definitions in mathematics.
You might also want to look at the following old thread in the math forum
I rather like the Lebesque covering dimension, because it defines the concept in very primitive spaces, called topological spaces, that need only the concept of a point and it's neighborhood. This is a much more basic concept (IMO) than a vector space.
The idea that a n-dimensional object is the boundary of a n+1 dimensional object is also an appealing way to define dimension, and is discussed somewhat in the above thread. Thus a line bounds a point, if you take a point out of a line it divides it into two parts. A line bounds a plane, etc, etc.
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