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2. Farey sequence - Wikipedia

   en.wikipedia.org/wiki/Farey_sequence

   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 ...

3. Harmonic series (mathematics) - Wikipedia

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

   Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...

4. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . A continued fraction is a mathematical expression that can be writen as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple ...

5. Harmonic progression (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Harmonic_progression...

   The first ten members of the harmonic sequence . In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.

6. Calkin–Wilf tree - Wikipedia

   en.wikipedia.org/wiki/Calkin–Wilf_tree

   i = 1081 = 10000111001 2: The continued fraction is [1;2,3,4,1] hence q 1081 = ⁠ 53 / 37 ⁠. i = 1990 = 11111000110 2: The continued fraction is [0;1,2,3,5] hence q 1990 = ⁠ 37 / 53 ⁠. In the other direction, using the continued fraction of any q i as the run-length encoding of a binary number gives back i itself. Example:

7. Tree (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tree_(graph_theory)

   A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2] A directed tree, [3] oriented tree, [4] [5] polytree, [6] or singly connected network [7] is a directed acyclic graph (DAG) whose underlying undirected graph is ...