The Great Pyramid of Giza built around 2560 BC is one of the earliest examples of the use of the golden ratio. The length of each side of the base is 756 feet, and the height is 481 feet. So, we can find that the ratio of the vase to height is 756/481=1.5717.. The Rhind Papyrus of about 1650 BC includes the solution to some problems about pyramids, but it does not mention anything about the golden ratio Phi.
Euclid (365BC - 300BC) in his "Elements" calls dividing a line at the 0.6180399.. point dividing a line in the extreme and mean ratio. This later gave rise to the name Golden Mean. He used this phrase to mean the ratio of the smaller part of this line, GB to the larger part AG (GB/AG) is the same as the ratio of the larger part, AG, to the whole line AB (AG/AB).Then the definition means that GB/AG = AG/AB.
The ratio between each triangle inside the triangle is 1.618 and that is the golden ratio. (Phi) Golden triangles are used in different shapes such as decagons or different pentagons, which are used in architecture.
The golden rectangle is the most desired ratio and most pleasing rectangle to look at. In architecture its used a ton and used in most building plans so that people will look at it and it will be pleasing to look at. Its display Fibonacci sequence because the ratio of the out side rectangle in all of Fibonacci ratio.