Abstract
In this paper, we introduce Farey triangle graph , Farey triangle matrix , complementary Farey triangle graph and complementary Farey triangle matrix , and we derive some properties of the following matrices.
Highlights
A Farey sequence of order N is a set of irreducible fractions between 0 and 1 arranged in an increasing order, the denominators of which do not exceed N
We introduce Farey triangle graph
In this paper we construct Farey triangle graph ( FΔG)N from ( (FΔG))N, in iterative process, and it is constructed from the method of mediant property as follows in the Farey sequence
Summary
A Farey sequence of order N is a set of irreducible fractions between 0 and 1 arranged in an increasing order, the denominators of which do not exceed N. In [1]-[3] Farey graph and Farey matrix have been constructed from Farey sequence of order N. In [4] Farey partition is derived and discussed some matrix property from Farey sequence. In [5] Farey graph is introduced in iterative process. In this paper we construct Farey triangle graph ( FΔG)N , in iterative process, and it is constructed from the method of mediant property as follows in the Farey sequence. From the co-ordinates of this graph we form a Farey triangle matrix We construct complementary Farey triangle graph ( F ∆G)N ′ and complementary Farey triangle matrix.
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