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2. Dimension (vector space) - Wikipedia

   en.wikipedia.org/wiki/Dimension_(vector_space)

   Dimension (vector space) A diagram of dimensions 1, 2, 3, and 4. In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. [1][2] It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.

3. Dimension - Wikipedia

   en.wikipedia.org/wiki/Dimension

   In mathematics. In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object.

4. Measure (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Measure_(mathematics)

   A simple example is a volume (how big an object occupies a space) as a measure. In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and ...

5. Four-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Four-dimensional_space

   Vectors. Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is.

6. Euclidean plane - Wikipedia

   en.wikipedia.org/wiki/Euclidean_plane

   For its applications, see Plane (physics). In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted or . It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines.

7. Metric space - Wikipedia

   en.wikipedia.org/wiki/Metric_space

   In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [ 1 ] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.

8. Three-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Three-dimensional_space

   Space has three dimensions because the length of a boxis independent of its width or breadth. In the technical language of linear algebra, space is three-dimensional because every point in space can be described by a linear combination of three independent vectors. Dot product, angle, and length. [edit]

9. Size - Wikipedia

   en.wikipedia.org/wiki/Size

   Size in general is the magnitude or dimensions of a thing. More specifically, geometrical size (or spatial size) can refer to three geometrical measures: length, area, or volume. Length can be generalized to other linear dimensions (width, height, diameter, perimeter). Size can also be measured in terms of mass, especially when assuming a ...