In this paper we will present a new exact formula for the fine-structure constant in terms of the golden angle,the relativity factor and the fifth power of the golden mean. A new interpretation and a very accurate value of the fine-structure constant has been discovered in terms of the golden radio. We propose the exact equivalent mathematical expression for the proton to electron mass ratio using Fibonacci and Lucas numbers and two other exact mathematical expressions for the proton to electron mass ratio. We present the exact mathematical expressions that connect the proton to electron mass ratio and the fine-structure constant. Also we will find a new formula for the Planck length and a new formula for the Avogadro's number. First we will find the beautiful unity formula that connects the gravitational coupling constant and the fine-structure constant. This equation is the simple unification of the gravitational and the electromagnetic interactions. We will present the exact mathematical formulas that connect six dimensionless physical constants. The six dimensionless physical constants are the proton to electron mass ratio μ,the fine-structure constant α,the ratio Ν1 of the electric force to the gravitational force between electron and proton,the Avogadro's number NA,the gravitational coupling constant αG of the electron and the gravitational coupling constant αG(p) of the proton. Also we will find a new formula for the gravitational constant G. Finally we will be presented the formula for the cosmological constant Λ. This unity formula is a simple analogy between atomic physics and cosmology. All these equations are simple,elegant and symmetrical in a great physical meaning.