Fibonacci Numbers and RosesEither, one of the most interesting or the dullest article about roses you will ever read!

I have never been fond of math or numbers. In high school I squeaked by with the minimum requirement for college entry. In college I was able to satisfy my degree requirement by taking a foreign language instead of a math. However, as a musician, math played an integral part in my young life and future career in music education.

In the early years of our marriage, my husband and I made regular trips to Sanibel Island in Florida. Sanibel is known for its great shell collecting and it is there that we fell in love with seashells. For years our home was adorned with both shells we had collected and specimens we had purchased to add to our collection.

Of the vast array of beautiful shell forms that nature has produced, the Chambered Nautilus became one of our favorites. We had books, photos and articles on this beautiful creature. One name kept appearing in various writings. Fibonacci.

Those many years ago the internet was not available. Today, if you Google Fibonacci, you quickly get 4,130,000 hits, give or take a few.

I can’t begin to explain the full scope of how the Fibonacci Numbers relate to nature and our daily lives but suffice to say, many things you look at and enjoy in nature exhibit this unique relationship between numbers and ratios.

Who Was Fibonacci?

Leonardo Pisano, or Leonardo of Pisa, was born in Italy around 1175. He was nicknamed Fibonacci, short for Filium Bonacci, or “son of Bonacci”. His home, Pisa, is also home to the famous “leaning tower”. Fibonacci was a well-known mathematician who traveled extensively and studied numbering systems that were in daily use during his lifetime. While still in his twenties Fibonacci began writing. He authored several hand written books which would bring him fame. All related to math and discussed addition, subtraction, multiplication and division in ways that were new to his time and location.

Probably his most important contribution to math was his recognition and promotion of the Hindu/Arabic number system in Europe. The system he encouraged and wrote about was based on ten digits: 1,2,3,4,5,6,7,8,9,0.

The incorporation of “0” was totally foreign to the accepted numbering systems of the day. He also introduced the floating decimal point.

Roman Numerals were the “status quo” for math at that time in Europe. Fibonacci’s books changed minds and convinced most in Europe that his new system was better. You can only imagine how profound a change this had on the world.

It Started With Rabbits!

The very special numbers (we will eventually get to) were observed when Fibonacci set out to determine how many rabbits would be produced from a single pair over the course of one year.

It is not completely clear why he began this study, but the problem and its solution were included in his famous book, Libra abbaci. What resulted was a set of numbers showing a ratio and relationship that would prove applicable to nature, symmetry and in general ……...to harmonious and pleasing relationships between things. Whether dealing with art, architecture, nature, animals and even body parts, the ratio or numbers can be observed.

One final name should be mentioned. Fibonacci never fully realized the importance of his discovery. It was not until the late 1800’s that a French mathematician, Edouard Lucas, assigned Fibonacci’s name to this unique set of numbers.

In fact, the same sequence had been discussed by Indian Scholars interested in rhythmic patterns prior to 1135, but Fibonacci and his rabbits brought the concept to more prominent attention and therefore he has been recognized for the ultimate discovery of their importance.

Drum Roll Please........Here Are The Numbers!

(0)1,1,2,3,5,8,13,21,34,55,89,144,233, 377, 610, 987, 1597...and it continues to infinity.

This might be a good time for our puzzle loving readers to try to figure out the relationship between the numbers. If you want to try, stop reading! If you concentrate on the first few you might have it pretty quickly.

This sequence of numbers is derived by adding the two previous consecutive numbers. 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, and so on. This was, in fact, the relationship that Fibonacci observed in the birthrate and reproduction of the rabbits in his study.

One of the most interesting aspects of this sequence of numbers is how often it occurs in nature. Fibonacci did not create or even understand the great significance of his discovery. He simply recorded the data that would, in time, be found to be present in our natural surroundings. Although the rabbit experiment has since been viewed as flawed, the sequence itself has been proven over and over to be correct and ever present.

Fibonacci Numbers In Nature:How They Apply

The Fibonacci numbers increase at a ratio that is revealed in objects and spirals. The Chambered Nautilus (which was so special to my husband and I) if cut in half reveals a series of chambers. Each chamber increases in size as the mollusk grows. They also grow in a spiral shape. This same spiral and ratio is present in a great many products of nature; the pinecone, the pineapple, the arrangement of seeds in the head of a sunflower, and so on. You can begin to see why many refer to the Fibonacci numbers as “the numbers of life”.

It gets even more fascinating. The ratio between all of these numbers after the first few combinations comes closer and closer to 1.618. This ratio ( 1.618 ) was considered by the Greeks and Romans to be a “Golden Section” or “divine proportion”. Most ancient Greek and Roman temples were built using these proportions. For example, many temples were designed to be 1.618 longer than they were wide. It gets even better. The Egyptian Pyramids were built with a base that was 1.618 times its height. Even the most attractive of human faces have been measured and bare these same proportions.

Finally………something that we can understand!

If any reader should decide to study Fibonacci further, references to Phi will become critical to the issue. The ratio between any two Fibonacci numbers is referred to as Phi. But for now, this writer will just stick with cherry (pie) and leave the Phi for you to read about elsewhere.

A few more ways that the Fibonacci numbers can be observed in nature follow.

The human body has one head, two eyes, ears, nostrils, arms, legs, five fingers on each hand, five toes on each foot, five senses, and so on. All are Fibonacci numbers. Studies of the human face have shown that facial features found by most to be attractive display dimensions containing the 1.618 ratio ( phi ).

The shape of the human ear most often depicts a Fibonacci spiral. The cochlea of the ear forms a Fibonacci spiral. The horn of a ram is in the shape of a Fibonacci spiral. The number of seeds and their placement within many fruits are Fibonacci numbers. And, one last example, DNA strands have Fibonacci spiral characteristics.

In simple terms, objects and things that we look at, (displaying these proportions) are pleasing to us.

Professionals in many fields have used this knowledge to create and design more successfully and we have taken great pleasure from what we see without knowing why.

The Spiral Shape

Fibonacci numbers reveal themselves most interestingly in the spiral shape of the rose bloom. We have all seen or taken countless photographs of a rose from above. We do this to observe that perfect center.

From that center, the petals flow outward growing wider and larger as they spiral. Even extensive hybridizing has not clouded this innate natural event. Those who are keen on exhibiting have been observing this phenomenon of nature each time they prepare a rose for a show. The term, Golden Spiral, was applied to the shape that evolved using a plan based on 1.618 or Phi. Again, further study will explain what Nature has done on its own.

The Golden Spiral is not only beautiful, it is functional. It has been determined that this arrangement allows for the most compact containment of the petals. Just think about the size of a rose bud compared to the size it achieves when fully open.

The Leaf Arrangement or Phyllotaxis

Again, the Fibonacci numbers are well represented in the arrangement of leaves on rose canes. Leaves on roses and most plants are arranged in a pattern that moves around and up and down in such a way that allows the maximum exposure of each leaf to moisture and sunlight.

Fibonnaci numbers are present in both the number of leaflets as they move around the cane and the number of times it takes before one leaflet is directly above the other.

As rosarians, we generally look to the next set of 5 leaves for deadheading. We will settle for 3 when necessary. Both are Fibonacci numbers. The number of leaves on various classes and varieties of roses is quite consistent and most often the number of leaves is a Fibonacci number. Yes, there are exceptions such as sets of 7, but they are far less common than sets of 5.

The Petals

Numerous references were made to wild roses containing 5 petals, which is a Fibonacci number. Also, regardless of their petal count, all roses have five sepals. Again, a Fibonacci number.

I reviewed the reported petal counts of over 300 roses and found few that had at or near one of the numbers in the famous sequence. In over 50 varieties I meticulously removed and counted the petals. Subjects studied were Hybrid Teas, Floribundas, Shrubs and miniatures. This seemed troublesome since the purpose of this article was to observe the presence of the numbers.

More About The Petals

However, after considering how we have hybridized roses over the years, I believe that we have actually subjugated the natural development of the roses in order to produce characteristics that are desirable. Nothing is wrong with that. It can be stated, however, that with the oldest roses the petal count is often found to be a Fibonacci number. Additionally, many mini’s and minifloras counted had 34 or 55 petals. Therefore, the numbers are still presenting themselves, regardless of man’s hand.

Conclusions

The sequence of numbers bearing Fibonacci’s name identifies the efficient arrangement of things in nature. What may seem random is anything but. His numbers appear so often that they can be termed a naturally recurring pattern. This subject is very far reaching, but it is fascinating to think about this set of numbers, this “divine proportion”, this ratio, and how often we can see it in our every day lives.

Perhaps the next time you are laying out a new rose bed, or deciding on how many plants to use, you will think about these natural numbers. I know that the next time you examine the center of a rose you will have a new insight on how that lovely spiral shape resulted. And, if nothing else, you can use the Fibonacci numbers to impress your friends and neighbors. By the way, in music there are 8 tones in a full octave and 13 tones in a chromatic octave. Very interesting!

The general laws of aesthetics, beauty and symmetry are not made, but have been defined by math and our good friend….Fibonacci.

All photos by Carol Green