What is the Fibonacci Sequence?

Let’s begin today’s Wonder of the Day with a game. We will display a series of numbers. Your task is to identify a pattern. Ready? Let’s begin:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

Can you spot the pattern? What will be the next number?

If you think the next number is 89, you are correct! You have just deciphered a pattern known as the Fibonacci Sequence.

What is the secret behind the Fibonacci Sequence? To find the next number in the sequence, simply add the two previous numbers together. This is how it works:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

… and so on! The Fibonacci Sequence goes on indefinitely.

The name “Fibonacci Sequence” originated from an Italian mathematician named Leonardo Fibonacci, who traveled the world in the early 13th century. During his travels, Fibonacci discovered different mathematical practices in other countries, particularly in India and the Middle East.

Upon returning to Italy, Fibonacci wrote a book called “Liber Abaci.” This book documented the mathematical knowledge he gained during his travels. It is in “Liber Abaci” where modern mathematicians first encountered the Fibonacci Sequence. However, Indian mathematicians were aware of this pattern centuries before Fibonacci wrote about it.

You might be wondering why the Fibonacci Sequence is still relevant today. Despite its ancient origins, this special pattern continues to be useful. It is sometimes used to make predictions. Traders, for example, employ the Fibonacci Sequence to forecast changes in the stock market. This helps us anticipate economic developments. In nature, the Fibonacci Sequence can be employed to predict the number of honey bees in a hive. Botanists also utilize it to estimate the number of petals that will grow on a flower!

Next time you visit the beach, take a closer look at seashells! The spiral shapes of certain seashells adhere to the Fibonacci Sequence. Mathematicians refer to this pattern as the Golden Spiral, which can be replicated by drawing a series of interconnected squares whose areas correspond to the numbers in the Fibonacci Sequence. Seashells are just one example of the Golden Spiral’s occurrence in nature. It is also evident in the arrangement of seeds on a sunflower, the positioning of seed pods on a pine cone, and even the shape of galaxies.

Observe your surroundings. Can you identify any other instances of the Fibonacci Sequence or the Golden Spiral? With a keen eye, you might uncover a new pattern of your own.

Try It Out

Are you ready to delve deeper into the Fibonacci Sequence and the Golden Spiral? Enlist the assistance of a friend or family member to explore the following activities:

  • Curious about Leonardo Fibonacci and the sequence that bears his name? Take a look at these 10 facts about Leonardo Fibonacci and the Fibonacci Sequence to learn more! In what other ways did Fibonacci influence the field of mathematics? Have you come across any other contributions by Fibonacci in your studies?
  • Fibonacci is credited with discovering the Fibonacci Sequence, but he actually learned about it while traveling in India! Read about more ways in which Ancient India influenced mathematics. Do you recognize any of these elements of Indian mathematics? How do you think modern mathematics would be different without the influence of ancient Indian mathematics?
  • Still intrigued by the Golden Spiral? Watch “Nature by Numbers” to visualize the Golden Spiral and gain a better understanding of its connection to the Fibonacci Sequence. Make sure to watch until the end for examples of the Golden Spiral in nature! Now that you have a deeper understanding of the Golden Spiral, can you think of any natural instances of it? Pay close attention to your surroundings—you might just discover the pattern in unexpected places!

References

  • https://www.mathsisfun.com/numbers/fibonacci-sequence.html (accessed on January 23, 2019)
  • https://plus.maths.org/content/life-and-numbers-fibonacci (accessed on January 23, 2019)
  • https://www.livescience.com/37470-fibonacci-sequence.html (accessed on January 23, 2019)

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