The detailed explanation is as follows:
1. Dimensions in mathematics:
Euclidean space: In Euclidean geometry, dimensions are usually used to describe the geometric shapes of points, lines, surfaces and solids. In three-dimensional space, three coordinate axes (x, y, z) are usually used to represent the position of points. High-dimensional space can be represented by more coordinate axes.
Vector space: In linear algebra, dimension is the maximum number of linearly independent vectors in vector space. For example, in a three-dimensional space, a set of linearly independent vectors can generate a three-dimensional vector space.
Manifold: In differential geometry, manifold is a topological space with the characteristics of local Euclidean space. Dimension describes the local topological structure of manifold, which can be integer dimension or fractional dimension.
2. Dimensions in physics:
Space-time dimension: the concept of four-dimensional space-time has been introduced into special relativity and general relativity, in which three dimensions describe space and the fourth dimension is time. These theories describe the space-time structure in the universe.
Multidimensional Universe Theory: Some physical theories, such as string theory, think that there may be more hidden dimensions in the universe, beyond the three-dimensional space and one-dimensional time we usually perceive.
3. Dimensions of computer science and data analysis;
Dimension of data set: In data analysis, dimension usually refers to the number of attributes or features in the data set. For example, the number of columns in a table can represent the dimension of a dataset.
High-dimensional data: High-dimensional data refers to data sets with a large number of characteristics or attributes. High-dimensional data analysis faces challenges, because with the increase of dimensions, the complexity of data and calculation will also increase.
4. Dimensions of social science and humanities:
Dimensional analysis: In social science, dimensional analysis is a method to measure and describe the relationship between multiple related variables. For example, personality psychology uses multi-dimensional methods to describe people's personality characteristics.
Cultural dimension: In cultural studies, dimensions are used to describe the differences between different cultures. The theory of cultural dimension put forward by Hofsbos describes the differences between different cultures in rights, individualism and collectivism, uncertainty and so on.
5. Dimensions of art and design:
Visual arts: In painting, sculpture and design, size is used to describe the size and shape of space. For example, a painting can be two-dimensional (plane painting) or three-dimensional (sculpture).
Multidimensional creation: Some artists and designers try to introduce multidimensional elements into their works to create more complex and abstract works.