2006-08-08 00:20:35 · 17 answers · asked by Goat 2 in Science & Mathematics ➔ Mathematics
A point is the intersection of an infinite number of dimensions.
A line is the intersection of two planes.
2006-08-08 01:23:47 · answer #1 · answered by blind_chameleon 5 · 0⤊ 0⤋
A point in Euclidean geometry has no size, orientation, or any other feature except position. Euclid's axioms or postulates assert in some cases that points exist: for example, they assert that if two lines on a plane are not parallel, there is exactly one point that lies on both of them. Euclid sometimes implicitly assumed facts that did not follow from the axioms (for example about the ordering of points on lines, and occasionally about the existence of points distinct from a finite list of points). Therefore the traditional axiomatization of point was not entirely complete and definitive.
Intuitively one can understand a location in the Cartesian 3D space. This location could be described with three real number coordinates: for instance
P = (2, 6, 9).
But one can also describe points in 1, 2 or more than 3 dimensions. The description of a point is quite similar to the description of a spatial vector, which also can exist in space with dimensions from one to many.
The conceptual difference between these notions is significant, though: a point indicates a location, while a vector indicates a direction and length. If a distinguished point (the origin) is given, one can describe a location by giving the direction and distance from the origin to that point.
2006-08-08 07:27:15 · answer #2 · answered by Anonymous · 0⤊ 0⤋
None. Zero. A point, according to Euclid, is "that which has no length, breadth, or depth," meaning it can't be measured by any of the three spatial dimensions.
Moving up the dimensional scale:
0 dimensions = point.
1 dimension = line.
2 dimensions = plane.
3 dimensions = solid.
4 dimensions = hypersolid, I think.
5 or more dimensions = you're watching too much science fiction!
2006-08-08 07:51:21 · answer #3 · answered by Louise 5 · 0⤊ 0⤋
Are we talking literally about a point, or about a point in time? The difference is important. A point in time is a concept with one dimension ... time. Using a point in space as an example ... The string theory in physics postulates 11 dimensions. Normally we recognize only 4 dimensions ... height, depth, width and time. I would argue for 4 dimensions as the answer to this question and require the questioner to prove otherwise. I think I just hurt my brain!! LOL
2006-08-08 07:37:57 · answer #4 · answered by lollipop 6 · 0⤊ 0⤋
A point thinks it has an infinite number of dimensions. In fact, it thinks that it is all the dimensions that there ever were, that it is everything. But it really has dimension zero; it has zero measure. In the ultimate view of things, it is nothing. It thinks it's everything; it really is nothing (except itself). Before you get too big an ego, consider the point.
2006-08-08 15:24:09 · answer #5 · answered by alnitaka 4 · 0⤊ 0⤋
A point is undefined. How can you talk about the dimensions of something that is undefined?
alnitaka: How interesting! I did not know a point could think? Huh, how did you discover this? You ought to write a paper on the subject - they might award you a PhD.
2006-08-08 14:57:49 · answer #6 · answered by Anonymous · 0⤊ 0⤋
A point is a zero dimensional space. This is actually part of the inductive definition of dimension.
2006-08-08 07:43:43 · answer #7 · answered by mathematician 7 · 0⤊ 0⤋
The concept of a single mathematical point has no dimensions.
2006-08-08 07:48:41 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Zero. In normal space, its location has three dimensions; the point itself has none since no number is needed to describe its size.
2006-08-08 07:25:30 · answer #9 · answered by Anonymous · 1⤊ 0⤋
An authentic mathematical "point" is a dimensionless object.
An every day point you would do with a pencil has 3 dimensions (under a microscope, it would have length, width and thickness)
2006-08-08 07:25:50 · answer #10 · answered by Vincent G 7 · 0⤊ 0⤋