DC Mathematica 2017

There is a special relationship between the golden ratio and Fibonacci sequences, e.g.: 0, 1, 1, 2, 3, 5, 8, 13, 21 ... where each number is the sum of the previous two numbers. These are called Fibonacci numbers 1 . If we take any two Fibonacci numbers in sequence and calculate their ratio, we find the result is very close to the golden ratio 2 . For example, in Figure 2, below, we calculate the ratio, it is initially close to the golden ratio. As we calculate the ratios of higher pairs the result comes closer to 𝜑 .

b

a

a/b

2

3

1.5

3

5

1.66666…

5

8

1.6

8

13

1.625

144

233

1.6180555…

233

377

1.6180257…

377

610

1.6180371…

fig. 2: Table of Fibonacci number

Having looked at the principles of the Fibonacci sequence and golden ratio, I will explain how two representative architectures have been built by these principles in both ancient and modern times.

The Parthenon

A major building of the ancient world that applies the Fibonacci sequence and the golden ratio is the Parthenon. Figure 3 shows the number of golden rectangles in the Parthenon. You can draw a spiral (as indicated in the red line), which is called a golden spiral. The overall structure of the Parthenon is a special logarithmic spiral related to the golden ratio 5 . The Greeks were obsessed with the golden ratio and applied it when building the Parthenon because they thought it was aesthetically appeasing. This is because the golden ratio is present in the human body and nature influencing what humans view as aesthetically pleasing 6 . Apart from the overall structure, the Greeks also paid attention to build the columns of the Parthenon in golden ratio 7 as shown in Figure 4 below. In this way, the Greeks could make the structure of Parthenon distinctive, aesthetic, enormous, and grand looking since the Parthenon had a symbolic importance to them 8 .

fig. 3: The Parthenon

fig. 4: Columns in the Parthenon

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