We present a body of results that demonstrate that the golden section can be implemented in the design of evolving systems. Albeit we only develop the mathematics, both mathematician and computer expert should find the concept clear. Perhaps of particular interest to the number t...
Open access
Research Article10.9734/jsrr/2019/v22i630107
The proportiones perfectus law states that σ_x^y=(x+√(x^2+4y))/2 is a proportione perfectus if 1≤y≤x such that for an arbitrary positive integer , there exists an integer sequence defined simultaneously by the quasigeometric relation h_(n+1)=round(σ_x^y h_n ),n≥1 and the arithmet...
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Research Article10.9734/jamcs/2019/v31i330115
The a:k:m-Fibonacci sequence is defined recursively by . We introduce the generalized a:k:m-Fibonacci sequence with arbitrary integers and and study some important properties relating to the Pascal type triangle generated from this sequence. The results are extended to negative...
Open access
Research Article10.9734/ARJOM/2018/42751
The a:k:m-Fibonacci sequences and the a:k:m-Lucas sequences are introduced. The well-known k-Fibonacci and k-Lucas sequences become a particular case (a=m=1). One might be interested to meet the equally famous Jacobsthal sequence at 2,1. Our brief results capture the most impor...
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Research Article10.9734/ARJOM/2018/42293
Corrigendum for Asian Research Journal of Mathematics 6(2), 1-9, 2017 It has been drawn to the journal's attention that there is a corrigendum of the published paper. Therefore, following the 'SDI Correction and retraction policy' this Corrigendum was processed and approved....
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Research Article10.9734/ARJOM/2018/39964
The proportiones perfectus law is introduced. Let . By definition, in the spectrum 1≤ y ≤ x , is a proportione perfectus With so defined, for an arbitrary positive integer h1 it is shown that there exists an integer sequence Hn satisfying the quasi-geometric relation such...
Open access
Research Article10.9734/ARJOM/2017/36860
We introduce a “structure” of epic proportions – golden pyramid whose sacred geometry is “Fibonacci squared”. In terms of mathematical beauty, the golden pyramid will perhaps be found to be comparable to Pascal triangle.
Open access
Research Article10.9734/ARJOM/2017/29964