on new definitions related to golden ratio

‎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.