The Special Theory of Relativity and the Golden Ratio

We can write more natural phenomenon with the golden ratio equations. We will derive the golden ratio from a right-angled triangle. We will connect the golden ratio with hyperbolic functions. The same equation can be interpreted as a golden ratio, as a relativistic Doppler effect, and also as a recourse to a "Special Relativity Theory". With the right-angled triangle, we will connect the golden ratio with rapidity and pseudorapidity. We will see that the Lorentz transformation equations relating to the circle, and the Lorentz transformation equations relating to the hyperbola describe the same phenomenon. Both equations describe the hyperbolic world at the same time. With the mentioned right-angled triangle, we presented the rotation of the coordinate system in Euclidean space, with the arbitrarily chosen point. We will derive from the Einstein's equation (x' - ct') = p (x - ct), the p variable. And, we will derive from the Einstein's equation (x' + ct') = m (x + ct), the m variable. After that, we introduce the imaginary number in our equations.