The Golden Ratio And The Fibonacci Numbers

The Golden Ratio is often denoted by the Greek letter phi: φ. Its exact value is 1+52 which is approximately equal to 1.618.

In this chapter, we saw how successive quotients of the Fibonacci Numbers get closer and closer to the Golden Ratio:

11=1, 21=2, 32=1.5, 53=1.67, 85=1.6, 138=1.625, 2113=1.615, …

Many people believe that the Golden Ratio, Golden Rectangles, and the Fibonacci Numbers “appear” in the real world in places such as:

Art
Architecture
Nature
Please research at least one example of such an “appearance” in art, architecture, nature, or someplace else in the real world and post your findings.

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The Mona Lisa by Leonardo da Vinci is one of the most famous paintings in the world. It is believed that da Vinci used the golden ratio in the composition of the painting, specifically in the placement of the subject’s eyes, nose, and mouth.

If we divide the painting in half vertically, the golden ratio is found at the point where the eyes are located. This creates a sense of balance and harmony in the painting. The nose is also located at the golden ratio, dividing the upper and lower parts of the face in a visually pleasing way. The mouth is slightly lower than the golden ratio, which helps to create a sense of mystery and intrigue.

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In addition to the placement of the facial features, the golden ratio can also be seen in the overall composition of the painting. The landscape in the background is arranged in a way that follows the golden ratio, creating a sense of depth and perspective.

The use of the golden ratio in The Mona Lisa is just one example of how this mathematical ratio can be found in art. Many other famous paintings, such as The Birth of Venus by Sandro Botticelli and The Starry Night by Vincent van Gogh, are also believed to use the golden ratio in their composition.

The golden ratio is a fascinating mathematical concept that has been studied by artists and mathematicians for centuries. There is no scientific evidence to suggest that the golden ratio is inherently beautiful, but many people find it to be aesthetically pleasing. Whether or not you believe in the power of the golden ratio, there is no denying that it is a fascinating phenomenon that has been found in many different areas of art and design.

Here are some other examples of the golden ratio in art:

  • The Parthenon in Athens, Greece is a famous example of a building that is based on the golden ratio. The dimensions of the temple are carefully proportioned to the golden ratio, creating a sense of harmony and beauty.
  • The spiral staircase is another example of a structure that is often based on the golden ratio. The spiral staircase is said to be more aesthetically pleasing than a straight staircase, and it is also more efficient in terms of space.
  • The human body is also said to be based on the golden ratio. The proportions of the face, torso, and limbs are said to be based on the golden ratio, which is why many people find the human body to be so aesthetically pleasing.

Of course, not everyone believes that the golden ratio is actually present in these works of art and architecture. Some people believe that the golden ratio is simply a coincidence, and that there is no real evidence to suggest that it is actually used in their creation. However, the fact that the golden ratio has been found in so many different places, from the human body to the natural world, suggests that it is more than just a coincidence.

Whether or not you believe in the power of the golden ratio, there is no denying that it is a fascinating phenomenon that has captured the imagination of people for centuries. It is a reminder that there is often beauty and order to be found in the world around us, even if we don’t always recognize it.

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