Unity Formula that connect the Fine Structure constant and the Proton to Electron Mass Ratio

Abstract

In this paper will be presented the unity Formulas that connect the Fine Structure constant α and the Proton to Electron Mass Ratio μ. The equations are simple,elegant and symmetrical in a great physical meaning. At the beginning we will make a review of the last works. We will suggest the exact formula for the Fine Structure constant α with the Golden Angle and the Fifth Power of the Golden Mean and αlso we propose a simple and accurate expression for the Fine Structure constant α in terms of the Archimedes constant π. After we propose two exact mathematical expressions for the Proton to Electron Mass Ratio. It will be presented the mathematical Formula that connects the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν1 of electric force to gravitational force between electron and proton,the Avogadro number NA,the Gravitational coupling constant αG for the electron and the gravitational coupling constant of proton αG(p). Also we will find a new formula for the Avogadro number NA and a new formula for Gravitational Constant G. Ιt will be explained that the product μ⋅α-1 is one of the roots of the following trigonometric equation: 2·102⋅cos(μ⋅α-1)+132=0 (1) It will also be shown that another way to show this equation is the following exponential form of the equation: 102⋅(eiμ/α+e-iμ/α)+132=0 (2) This exponential form can also be written with the form: 102⋅(eiμ/α+e-iμ/α)=132⋅eiπ (3) So the beautiful formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and the Fifth Power of the Golden Mean is: 52⋅(5∙φ-2+φ-5)2⋅(eiμ/α+e-iμ/α)+(5∙φ2-φ-5)2=0 (4) Also the formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and Mathematical constants π,φ,e,i is: 102⋅(eiμ/α+e-iμ/α)=(5∙φ2-φ-5)2⋅eiπ (5) Also the unity Formula can also be written in the form: 10⋅(eiμ/α+e-iμ/α)1/2=13⋅i (6) Finally we will show that the radio ω=(c/υs)2 of the speed of light and the maximum speed of sound depends only from the Fine Structure constant α and not from the Proton to Electron Mass Ratio μ: 102⋅(eiωα/2+e-iωα/2)+132=0 (7) All these equations are simple,elegant and symmetrical in a great physical meaning.