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 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!
Can you figure out the next few numbers?
The Fibonacci sequence can be written as a "Rule “which is: xn = xn-1 + xn-2 The terms are numbered from 0 forwards as seen in the chart below. xn is the term number n. xn-1 is the previous term (n-1) and xn-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 stated previously, we come across Fibonacci numbers almost every day in real life. For instance, many numbers in the Fibonacci sequence can be linked to ordinary things we see around us such as the branching in trees, the arrangement of leaves on a stem, the flowering of an artichoke, or the fruitlets of a pineapple. In addition, numerous claims of Fibonacci numbers are found in common sources such as the spirals of shells or the curve of waves.
Fibonacci numbers can also be seen in the arrangement of seeds on sunflower heads. If you look at the seed arrangement in the center, you'll observe what looks like spiral patterns curving left and right or clockwise and counter clockwise. Incredibly, if you count the spirals, the total will be a Fibonacci number. Divide the sunflower spirals into those pointed left and right, and you'll get two consecutive Fibonacci numbers.
Many other plants in nature also illustrate this sequence. For instance, buttercups have 5 petals; lilies have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 while daisies can be found with 34 or 55 or even 89 petals.
Here are two questions to think about:
- How might knowing this number pattern be useful?
- What kinds of things can the numbers in the Fibonacci sequence represent?