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flat piece of paper we are drawing on a plane ... ... except that the paper itself is not a plane, because it has thickness! And it should extend forever, too. wht does this mean?
So, we're in a 3-dimensional world for all intents and purposes (actually anywhere between 4 and 11, but let's not get into that). Any object we see is 3-dimensional. Think of a cube - it's got length, width, and height, or you could say that it has extents in 3 different dimensions (each of which are orthogonal to the others). Another way to think of it is that you would need three numbers (coordinates) to describe the position of any point in space uniquely - it's 3-dimensional space. Take a dimension away and you end up with two orthogonal dimensions. Your cube turns into a square - draw a cube from the top, and you end up with a square, in 2 dimensions. You need 2 coordinates to describe the location of any point in 2-dimensional space. Now take another dimension away. You'll end up with a line. It extends only along one dimension and doesn't need another dimension to be a line. A single number can describe the location of any point along that one dimension. You could go one further and take the last dimension away, and you end up with a point ;)
the the coordinate x and yaxis?
Yea - in 2 dimensions, you could imagine the dimensions like the axes of a coordinate system. So, for a 2-dimensional system you need two numbers, for 3 dimensions 3 coordinates to describe a location. Add a fourth dimension and you need 4 numbers - think of time as a fourth dimension, and to describe any event uniquely you need to be able to tell where (x,y,z) and *when* it happened (t). So, for 4 dimensions you'd need 4 coordinates to describe the location of any point. In 0 dimensions there are no coordinates, because there are no dimensions and no extents.
thanks opiesche.......does the room have 3 dimensions?
Yes, a room would have three dimensions. So would a cube or a sphere. Another way to visualize the 'taking away' of a dimension would be this: Place a cube (3-dimensional) in front of a wall and shine a flash light on it. You'll see the shadow of the cube on the wall - in 2 dimensions. The shape of the shadow changes as you move the flash light around, but it's always in 2 dimensions. The shadow is, in fact, a 2-dimensional projection of the 3-dimensional cube.
Now imagine you could take another flash light , shine it down straight from the top of the shadow and have the 2-dimensional shadow itself cast its own shadow on the floor (it's not possible, of course, but just imagine for a second it would be). You'd see the two-dimensional shadow cast its own shadow on the floor, and that shadow would be a line - it would be one-dimensional. It would be a one-dimensional projection of the 2-dimensional shadow ;)
thats okay and why is a circle 2 dimensional?
This is going to sound strange, but because it doesn't need a 3rd dimension to be a circle. You could place it in 3 dimensions, but really, all you need to describe a circle are two dimensions - the x and y coordinates that lie on the circle at a certain distance away from the radius. If you add a Z coordinate to the location on the circle (extrude the circle upwards), it would become a cylinder.
that was supposed to say 'a certain distance away from the center.'
You could say that what defines how many dimensions an object has is determined by how many coordinates you need to describe any location on it. For a circle or square you need exactly two.
u knw a lot
do u need to be imaginative to be good at this stuff?
It doesn't hurt to be able to visualize. I'm better at that than I am at formalizing these concepts ;) BTW, this is a really good (albeit old and maybe a little cheesy) exploration of dimensionality: http://www.youtube.com/watch?v=KIadtFJYWhw Carl Sagan was awesome.