Fibonacci Numbers and Roses
Either, 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.
The incorporation of “0” was totally
foreign to the accepted numbering
systems of the day. He also introduced
the floating decimal point.
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.
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.
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.
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.
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.
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.
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