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Research Articles Issue 2 · 2024 · pp. 101–111 · Issue page

NEW FIBONACCI SERIES THE OTHER SIDE OF THE COIN

MU
Muhammed DEMİR1
1 Mathematics Teacher, Ministry of National Education, Turkey
Corresponding author: [email protected]
DOI https://doi.org/10.38173/RST.2024.28.2.9:101-111
Received 23 August 2024
Revised -
Accepted 05 November 2024
Available Online 15 November 2024
Abstract
IT IS KNOWN THAT THE FIBONACCI SEQUENCE IS USED IN DOZENS OF FIELDS SUCH AS FINANCE, NATURE, ART, CRYPTOGRAPHY, MUSIC AND ECONOMY. THEY ARE FINDING THE (N)T H ELEMENT IN THE FIBONACCI SE QUENCE REQUIRES CALCULATING THE (N -1) AND (N -2) ELEMENTS. THE FIRST AND SECOND ELEMENTS ARE CALCULATED RECURSIVELY. THE FIBONACCI SEQUENCE IN THIS STUDY IS ASCERTAINED USING THE PASCAL TRIANGLE. A FORMULA FOR DIRECTLY DETERMINING THE NECESSARY FIBONACCI ELEMENT HAS BEEN PROPOSED. WHEN ALL OF THE ELEMENTS IN THE DIAGONAL PLANE ARE GATHERED IN PASCAL TRIANGLES FROM LEFT TO RIGHT, IT IS KNOWN THAT THE ELEMENTS OF THE SEQUENCE KNOWN AS FIBONACCI CAN BE CALCULATED SEQUENTIALLY. THE HIDDEN PATTERN WITHIN THIS TRIANGLE IS CONVERTED INTO A NEW FORMULA BY UTILIZING MATHEMATICAL FUNCTIONS, SIGMA SYMBOLS, AND COMBINATION MODELING. RECURSION AND DYNAMIC PROGRAMMING COMPUTATIONS YIELD THE MINIMAL TIME AND SPACE COMPLEXITY TO FIND THE FIBONACCI SERIES.
Keywords
FIBONACCI SEQUENCE GOLDEN RATIO RECURSION FORMULA
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