The Kepler Triangle

The Great Pyramid of Giza, figure (3a), is one of the Seven Wonders of the Ancient World and also a symbol of Egypt. It was built in 2650 BCE and was considered to be the tallest structure ever made by human hands. By looking at a cross section through a pyramid, one can notice a triangle. This triangle in the Great Pyramid is known as the Triangle of Price or the Kepler triangle (shown in figure 3b).

The Kepler Triangle is a right triangle with “edge lengths in geometric progression.” With figure (3b), the slant height is phi, the base is one, and the height is the square root of phi. It is a ratio of 1: 1.272:1.618, because when the variables are squared by the pythagorean theorem, an individual can receive the quadratic equation where

As said above, within the Kepler Triangle, the ratio of the slant height to the base, Φ1, is equal to the golden ratio as dividing the slant height (S) by half the base. Using the calculations mentioned, it results in relatively 1.61804, which means that there is a slight difference of 0.00001.

Φ=Φ1≅S(1/2) of the base≅ 186.369m115.82m≅ 1.61804

Despite the slight difference in these numbers, this demonstrates that the Egyptians were capable of integrating the Golden Ratio into their structures, as it was one of the first famous buildings created by the human

It is one of the most important surviving buildings of Ancient Greece and was created in 447 BC. The Golden Ratio allows the Parthenon to be beautifully crafted and aesthetically pleasant. From the base to the edge of a column to the bottom of the roof, it is relatively in proportion with the golden ratio.

Within figure four,

PEPA= 19.87 meters12.28 meters ≅ 1.61807 and PAAE= 12.28 meters7.59 meters≅ 1.61792

Therefore, PEPAis approximately equal to PAAE.

To convert the differences from the theoretical value, which is the approximated value of the golden ratio, one can take the theoretical value minus the experimental value and then divide that by the theoretical value. Using the number given, finally multiply by 100% to produce a percent. If the result is a negative for the percent, then the absolute value of the number has to be taken as shown below.

PEPA= (1.61803 - (19,89 meters 12.28 meters)1.61803) x 100% = 0.0025%

PAAE= (1.61803- (12.28 meters7.59 meters)1.61803) x 100% = 0.0068%

These percentages indicate that the architects who had built the Parthenon had used the concept of the golden ratio is there structure. It also demonstrates that from the actual theoretical value of the golden ratio, there is only a slight difference between the theoretical and experimental value which was the reason for the very small percentage.