On New Definitions Related to Golden Ratio

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Pakdemirli Mehmet

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Journal Paper

Paper Information

Journal: Mathematics Interdisciplinary Research Year:2025 | Volume:10 | Issue:2 Page(s): 145-158

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Information Journal Paper

Title

On New Definitions Related to Golden Ratio

Author(s)

Pakdemirli Mehmet | Issue Writer Certificate

Keywords

Fibonacci sequence‎

‎tree‎

‎Elastic collision‎

‎Damped systems‎

‎Spirals‎

‎Heart

Abstract

‎New definitions employing the golden ratio as the characteristic parameter are proposed. The definitions are classified into two categories: Geometrical and Physical properties‎. ‎In the first category‎, ‎the golden ratio tree is defined‎, ‎and its properties are discussed through theorems‎. ‎Then‎, ‎decaying and growing type golden ratio spirals are proposed and discussed‎. ‎The equation producing the golden ratio heart in the analytical two-dimensional space is given‎. ‎Regarding the second category‎, ‎the golden ratio ball is defined with respect to collisions with the ground and the collision coefficient is determined‎. ‎Golden ratio damping is another new definition in which the dimensionless damped parameter is determined in terms of the golden ratio‎. ‎Theorems are posed and proven regarding the properties of the definitions‎. ‎Numerical solutions in the form of plots are given when necessary‎.

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