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Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
Aryabhata II. Āryabhaṭa (c. 920 – c. 1000) [1] also known as Arya Diya Jankhi was an Indian mathematician and astronomer, and the author of the Maha-Siddhanta. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I. Scholars are unsure of when exactly he was born, though David Pingree dates ...
Sometimes the term "unit cube" refers in specific to the set [0, 1] n of all n-tuples of numbers in the interval [0, 1]. The length of the longest diagonal of a unit hypercube of n dimensions is , the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space. See also
The cube rule or cube law is an empirical observation regarding elections under the first-past-the-post system. The rule suggests that the party getting the most votes is over-represented (and conversely, the party getting the fewest votes is under-represented). It was first formulated in a report on British elections in 1909, then extended to ...
Roth's theorem on arithmetic progressions. Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the natural numbers. It was first proven by Klaus Roth in 1953. [1] Roth's theorem is a special case of Szemerédi's theorem for the case .
The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first [dubious – discuss] described ...
OLAP cube. An OLAP cube is a multi-dimensional array of data. [1] Online analytical processing (OLAP) [2] is a computer-based technique of analyzing data to look for insights. The term cube here refers to a multi-dimensional dataset, which is also sometimes called a hypercube if the number of dimensions is greater than three.