 ## Due to inclement weather, please call us at 847.749.3922 to check whether we are open. Sorry for the inconvenience. # What Are Fibonacci Numbers, And Why Are They Everywhere?

Fibonacci numbers are numerical sequences that are closely related to the golden ratio. These numbers reappear in nature and science. It’s no surprise why — they’re beautiful. Fibonacci numbers have been widely used by historians, architects, mathematicians, scientists, and other creative individuals. These users have discovered many uses for the numbers themselves as well as applications that utilize ratios found within Fibonacci numbers. This article will provide an overview of Fibonacci numbers and what they have to do with everything.

#### What Are Fibonacci Numbers?

Fibonacci numbers are a sequence of numbers that can be found in nature. The first two numbers in the sequence are 0 and 1, which you can think of as the seeds for the next number in the series. The next two numbers in the sequence are 1 and 1, or 1 and 2, which gives us the next two terms of the sequence: 1, 1, 2, 3, 5, 8, and so on.

You can find these numbers everywhere! They describe everything from leaves on trees to sunflowers to pinecones. They’re even used to describe rabbit populations! The Fibonacci sequence is one of the most famous sequences discovered by mathematicians.

#### The formula is simple, but the results are extraordinary.

Fibonacci numbers are a series of numbers that come up in many different places. They are also called the Fibonacci sequence and were named after Leonardo of Pisa, a famous Italian mathematician.

The formula is simple, but the results are extraordinary. Let’s take a look at how it works:

Step 1: Start with the number 0 and add 1, then add 1 to that result. This gives us 1 and 2, or 0+1=1, which is called the first Fibonacci number.

Step 2: Repeat step one again, this time adding 2 instead of 0 (1+2=3). We now have three consecutive Fibons: 0+1+2=5. This can be continued indefinitely by adding two more numbers at each step to get any number between 1 and infinity. The sum of all these numbers is called a “Fibonacci sequence.”

#### Why Are They Everywhere?

Fibonacci numbers are everywhere. They’re in nature and our mathematics. They are found everywhere in nature, from the spiral growth of a plant to the sinusoidal shape of waves on a lake, to the way pinecones grow and the petals of flowers open and close in the wind.

The Fibonacci sequence is so important that it’s been used as a navigation tool for centuries by sailors who needed to know how long it would take them to reach their destination or how much time they had left before the high seas made their journey impossible. It’s also used by astrologers and numerologists who believe that certain numbers hold special meaning for us all.

In mathematics, Fibonacci numbers are used more often than any other sequence of numbers. They’re everywhere, from biology and chemistry to economics, engineering, and even psychology. Even though there are different types of Fibonacci numbers out there, they’re all based on the same concept: adding each number after the previous one by adding 1 or adding 0.

#### Examples Of Fibonacci Numbers In Nature

##### Pinecones

Pinecones have a very interesting property; the Fibonacci numbers are found in the patterns. The pine cones are no exception. Pine cones have spirals that grow longer and longer. The spiral gets larger and larger until it reaches the end of its growth period, then it starts all over again.

Pine cone spirals can be seen on many different plants, but they are most commonly found in pine trees. They can also be found in other plants such as ferns and sunflowers. Pine cone spirals are also quite common in nature in many other places, such as seashells and shells. In fact, you can find Fibonacci numbers in all of these places, except nature doesn’t grow pinecones or seashells!

##### Sunflowers

The sunflower is a favorite example of the Fibonacci sequence because it grows in an ideal way. The first pair of leaves sprout from the stem at one end, the second pair at the other end, and then each pair in between. The next set of three flowers grows after that and so on until you get a series of five flowers on each stem (the “flower-bud-flesh” pattern).

How do you know this? Because if you look at any sunflower seed pod under a microscope, you’ll see that they contain 25 pairs of seeds. The first two pairs are leaf buds, which eventually sprout into two more leaves; each pair in between is a single leaf; the final pair is the petal that forms along with its associated stigma (which may or may not be fertilized).

##### Peacocks

Peacocks are an example of a Fibonacci number. They have a unique tail feathering pattern repeated every two to three feathers.

The peacock’s tail feathers were measured in the 19th century to create a mathematical formula that described how peahens select their mates. This is called “Fibonacci’s Law,” and it describes how numbers grow based on each other. Each new number is created by adding the two previous ones together, and the sequence always starts with 1 and 1 again when you count from left to right.

##### Cactus

Cactuses are a good example of Fibonacci numbers. They have spiraling growth patterns that repeat every 25-30 years, in which each new whorl is larger than the one before it.

Cactus seeds grow into cactus plants with spiraling whorls of branches, leaves, and spines. Each new whorl is larger than the one before it, and these spirals begin at the base of a plant. This is an example of Fibonacci numbers in action!