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2. Dimension (vector space) - Wikipedia

   en.wikipedia.org/wiki/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. Four-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Four-dimensional_space

   For example, consider the formulas for the area enclosed by a circle in two dimensions (=) and the volume enclosed by a sphere in three dimensions (=). One might guess that the volume enclosed by the sphere in four-dimensional space is a rational multiple of π r 4 {\displaystyle \pi r^{4}} , but the correct volume is π 2 2 r 4 {\displaystyle ...

4. Geometry - Wikipedia

   en.wikipedia.org/wiki/Geometry

   Mathematics. Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2] Geometry is, along with arithmetic, one ...

5. Vector (mathematics and physics) - Wikipedia

   en.wikipedia.org/wiki/Vector_(mathematics_and...

   Infinite-dimensional vector spaces occur in many areas of mathematics. For example, polynomial rings are countably infinite-dimensional vector spaces, and many function spaces have the cardinality of the continuum as a dimension. Many vector spaces that are considered in mathematics are also endowed with other structures.

6. Dimension - Wikipedia

   en.wikipedia.org/wiki/Dimension

   A tesseract is an example of a four-dimensional object. Whereas outside mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions", mathematicians usually express this as: "The tesseract has dimension 4", or: "The dimension of the tesseract is 4" or: 4D.

7. Fractal - Wikipedia

   en.wikipedia.org/wiki/Fractal

   In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set.