Mathematical dimension:
The common understanding is that "a point is 0-dimensional, a straight line is 1 dimensional, a plane is 2-dimensional, and an object is 3-dimensional". In fact, the concept mentioned in this statement is "premise" rather than "described object", and all described objects are "points". Therefore, its complete expression should be "the point based on point is 0 dimension, the point based on line is 1 dimension, the point based on plane is 2 dimension, and the point based on volume is 3 dimension". Further explanation, the point on the description (positioning) point is the point itself, and no parameters are needed; Describing (locating) a point on a straight line requires 1 parameters (coordinate values); Describing (locating) a point on a plane requires two parameters (coordinate values); Describing (locating) a point on a volume requires three parameters (coordinate values). If you change the "object", you will get different conclusions, such as: "A straight line is 4-dimensional based on a plane, 6-dimensional based on a straight line, and 9-dimensional based on a plane". Further explanation, two points can determine a straight line, so describing (locating) a straight line requires 2×2 parameters (coordinate values) on the plane and 2×3 parameters (coordinate values) on the body; A plane can be determined by three points of a line, so 3×3 parameters (coordinate values) are needed to describe (locate) a plane on an object.
2. Physical dimensions:
For example, two parallel lines can be regarded as two relatively independent one-dimensional spaces. If you want to go from one line to another, you need to create a new straight line to connect them. This straight line is the dimension. Dimension 0 is a point and has no length. 1 dimension is a straight line with only length. 2D is a plane, which is the area formed by length and width (or curve). Three dimensions are the volume formed by two dimensions plus height. /kloc-in the 9th century, mathematicians discovered fractal, thus creating a new dimension-"fractal dimension", from which people realized that dimension is not only an integer, but also a fraction or even an irrational number. Professor Stephen Hawking, a famous British physicist, has this explanation: it is like a hair, which is a one-dimensional line from a distance. Under the magnifying glass, it is really three-dimensional; If we face time and space, if we have a magnifying glass with high magnification, we should also be able to reveal other possible 4-and 5-dimensional spaces, up to 1 1 dimensional space.