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emekwuluA set of numbers like 0, 2, 4, 6, 8, 10… increases uniformly in twos. Therefore, it exhibits a pattern. A set of numbers like the one above is also called a sequence. A sequence can take forms other than the example given above.

On the night of Tuesday, March 30, 1993, I had a dream where I saw a partial floral representation of the Fibonacci sequence. For those not familiar with the Fibonacci sequence, it runs like this: 1,1, 2, 3, 5, 8, 13, 21, 34…. This sequence was discovered by an Italian mathematician named Fibonacci, and each of the numbers is called a Fibonacci number. The pattern is: x, y, x + y. One outstanding property of this sequence is that the next term in it is a sum of the two preceding terms: 1 + 1 = 2, 1 + 2 = 3 , 2 + 3 = 5 , 3 + 5 = 8.

The following morning I took a piece of paper and a pen and started to write. Initially I thought it would have been an article of about 20 pages. I was wrong. As days passed by, the more I played with those numbers, the more I discovered properties of the sequence. The properties are as exciting as they are interesting. So I ended up with about 150 pages of material out of sheer inspiration.

Numbers of the Fibonacci sequence have many properties. Fibonacci numbers appear in nature. They have applications in arts, architecture, artificial intelligence, and other fields. But discussing these and other properties is not the objective of this article.

Most exciting to me in this dream experience was the transformation of consciousness. During and after the dream experience, I was extremely calm, peaceful and serene. I am at a loss for words to describe my actual experience, but I have never, in my years of existence on this planet, attained that level of consciousness. It was amazing. This experience eventually resulted to a book on Fibonacci numbers. It has about 140 pages.

Some people have started to wonder where they can see Fibonacci numbers and why I am so fascinated with Fibonacci numbers?

emekwulu-daisySome Real-Life Applications of Fibonacci Numbers

  • In well-proportioned human beings, the ratio of the length from the navel to the forehead to the length from the navel to the feet is equal to the golden ratio, 1.6180.
  • The number of petals and sepals of most beautiful flowers are all numbers of the Fibonacci sequence e.g. Alamanda, Hibiscus, Columbine.
  • The arrangement of seeds in the sunflower presents an interesting pattern. They appear to be spiraling outwards both to the left and the right. There is a Fibonacci number of spirals.

emekwulu-parthenonFibonacci numbers and Architecture
The golden ratio — known to the Greeks of the old — is normally denoted by the Greek letter Phi (1.6180). The Greek mathematicians of the time of Plato (about 400 BC) recognized it as a significant value and Greek architects used the ratio as an integral part of their designs, the most famous of which is the Parthenon in Acropolis, Athens. The Parthenon was started in 447 BC and finished in 432 BC.

Fibonacci Numbers and the Golden Section
An interesting and a special value closely related to the Fibonacci series is called the golden section. The golden section is obtained by taking the ratio of successive terms of the Fibonacci series. As n gets larger and larger, this ratio approaches an interesting limit. This limit is actually the positive root of a quadratic equation and is called the golden mean, or sometimes the golden ratio or still divine ratio.

The Beauty Equation and Fibonacci Numbers
In a study to measure attractiveness, Dr. Kendra Schmid, assistant professor of Biostatistics in the College of Public Health at the University of Nebraska Medical Center, says there is a “perfect face.” Her study used geometry to measure attractiveness on a scale of 1 to 10. She uses the golden or divine ratio and 29 other factors to study what she calls facial sex appeal. Other factors used in the study include symmetry. The study shows that as the ratio of the length of the face to the width of the face gets closer and closer to the golden ratio, both male and female images were viewed as more attractive. As defined by the golden ratio, the ideal result is 1.6.

Dr. Schmid’s study used 36 participants of Caucasian faces (18 males, and 18 females). She has been on The Oprah Winfrey Show discussing “Sex: Women Reveal What They Really Want.” She is also a part of a two-hour documentary on the Discovery Channel entitled, “The Science of Sex Appeal.” Dr. Schmid’s research was published in Pattern Recognition magazine in August 2008.

I was so fascinated with Fibonacci numbers that on this night I dreamed of curative or healing Fibonacci Numbers. In the dream, they were defined as Fibonacci Numbers that under certain conditions, when uttered, generate healing energies in the body capable of providing a cure for certain ailments. Curative Fibonacci numbers are therefore, much like mantras — vowel sounds that when uttered tend to produce some physiological changes in the body, as evidenced in transcendental meditation, a technique that centers on the use of mantras and aims to bring about a state of tranquility.

Future Research on Healing Fibonacci Numbers
To my knowledge, not much research has been done in this area. Any such future research should involve mathematicians, parapsychologists and medical doctors with inclination to alternative healing therapies.

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Paul Chika Emekwulu was born in Ekwulobia in southeastern Nigeria. His books, articles and activities have been reviewed, published and featured in Nigeria and in several U.S. newspapers and magazines. His interests include the paranormal, exploring properties of triangular numbers and Fibonacci numbers. He independently developed a mathematical formula connecting triangular numbers and numbers of the Fibonacci sequence. Emekwulu has spoken at several schools and organizations, and he has been a guest on several radio and TV stations.

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