فهرست نشریات علمی دسترسی آزاد ایران

‎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.