Examining Fibonacci Numbers

Fibonacci

Even if you were taught about the Fibonacci number sequence in school, you probably don’t remember much about it. As with other higher levels of math, many aren’t sure how Fibonacci could possibly be relevant to their real lives; so, why should they even attempt to remember him or his sequence? In reality, Fibonacci numbers are something you come across practically every day. Even so, let’s go back and start at the beginning.

The Fibonacci number sequence is named after Leonardo of Pisa (1175-1240), who was known as Fibonacci. (I love to say that name because it sounds like I know a foreign language.) In mathematics, Fibonacci numbers are this sequence of numbers:

As you can see, it is a pattern, (all math is based on patterns). Can you figure out the number that follows 89? Okay, let's pretend I waited for at least 60 seconds before giving you the answer….144. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. For those who are still having difficulty (like my daughter who is sitting here), it is like this.

  

The next number is found by adding up the two numbers that precede it.

• The 8 is found by adding the two numbers before it (3 + 5)
• Similarly, 13 is found by adding the two numbers before it (5 + 8),
• And the 21 is (8 + 13), and so on!

It is that simple! For those who just love patterns, here is a longer list:

 

Can you figure out the next few numbers?

The Fibonacci sequence can be written as a "Rule “which is:   x_n = x_n-1 + x_n-2   The terms are numbered from 0 forwards as seen in the chart below.   x_n is the term number n.   x_n-1 is the previous term (n-1) and x_n-2 is the term before that (n-2)

Sometimes scientists and mathematicians enjoy studying patterns and relationships because they are interesting, but frequently it's because they help to solve practical problems. Number patterns are regularly studied in connection to the world we live in so we can better understand it. As mathematical connections are uncovered, math ideas are developed to help us be aware of the relationship between math and the natural world. 

As I close, here are two questions to think about:

1. How might knowing this number pattern be useful? 
2. What kinds of things can the numbers in the Fibonacci sequence represent?