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In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [ a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...
, 2 H, and 3 H. 1 H and 2 H are stable, while 3 H has a half-life of 12.32(2) years. [3] [nb 1] Heavier isotopes also exist, all of which are synthetic and have a half-life of less than one zeptosecond (10 −21 s). [4] [5] Of these, 5 H is the least stable, while 7 H is the most.
100 120° (4 cycles) In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,..., n which repeat until the figure closes. The number of repeats needed is called its cycles. [ 1] A simple spirolateral has only positive angles.
Percolation threshold. The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.
In the mathematical field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who introduced one of the models in 1959. [ 1][ 2] Edgar Gilbert introduced the ...
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring.
The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number.
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that. an alternating series . It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series ), [ 1] and was later ...