Fibonacci Sequence - The Magic of Nature

Today's date is 11/23. Do you notice anything different about it? Keep reading to find out! The Fibonacci Sequence is a set of numbers where the sum of 2 previous numbers gives the next number. For example, let's consider a set 4, 8, 12, 20, 32, 52. We can see that, 4+8=12, 12+20=32, 20+32=52. So, this is a Fibonacci sequence. And since today's date follows this same pattern, November 23 is Fibonacci Day!

The Origin Story

This sequence is named after the Italian Mathematician, Leonardo Pisalo Bigollo, whose nickname is Fibonacci. But, he didn't discover it. He spread the idea to the Westerners through his work, "Book of Calculation". He learned it while growing up in North Africa. Since his father was a merchant, he learned the Hindu-Arab numerals instead of Roman numerals which was much easier for their bookkeeping. The first record of the Fibonacci sequence was explained in 200 BC by Acharya Pingala, an Indian mathematician, and poet. He identified possible patterns of Sanskrit poetry formed from syllables of two lengths.

The Golden Ratio

The special thing about this is that any number in the Fibonacci sequence (ignoring the first few numbers) divided by the previous number is always 1.6. Let's take another sequence 6, 12, 18, 30, 48, 78. Ignoring the first 2 numbers, 30 divided by 18 is 1.667, 48 divided by 30 is 1.6, and 78 divided by 48 is 1.625. This means that each number is 1.6 times higher than the previous number. As the series goes on, the ratio seems to be exactly 1.618 but actually never reaches it. This number, 1.618 is called the Golden Ratio or phi. The Greeks used this to build The Golden Rectangle, which is a rectangle with sides having consecutive Fibonacci numbers. It is especially significant in architecture, the most notable ones being, the Pantheon and the Great Pyramid at Giza.

Significance of The Golden Ratio in Nature

Fibonacci Sequence is also known as "nature's universal rule" or "nature's secret code". It's found in the way seeds are arranged in a flower and even in the number of petals in a flower. The seeds spiral outwards with numbers usually matching the Fibonacci numbers. Since the seeds are so tightly packed, there is a lower chance of them getting damaged. Sunflowers and daisies are great examples of this. You can also find it in the way the scales of pinecones and the fruitlets of pineapples are arranged. In trees, the pattern in which the trunk splits into branches follows the Fibonacci sequence too.

The golden ratio pops up in animals too. If you divide the number of females in a colony by the number of males, the answer is mostly 1.618. And in the bee family tree, the number of male's parents and grandparents is 2, 3, 5, 8. This applies to the females too but the number is 2, 3, 5, 8, 13. In humans, if you measure the section of each finger, it's approximately 1.6 times bigger than the previous section. Even our DNA follows the rules of the Fibonacci code. If you divide the length and breadth of DNA molecule, which is 34 and 21 angstroms, it approximates to phi.

Activities for Kids Using Fibonacci sequence

Kids get a deeper and better understanding of things by applying what they've learned to their daily life. So, we can start by explaining the basics of the Fibonacci sequence, giving them examples, and then encouraging them to look around and find things that follow this rule. They can collect their findings and trace out the patterns using markers. Or, they can glue glitter or sequins on them. After that, we can guide them to do a project using simple craft supplies like colored paper, pipe cleaners, and beads.

1. Cut out two 1 by 1 squares, then a 2 by 2 square, then a 3 by 3 square, and so on till 21 or more, depending on their grade.

2. Arrange the colored squares to form a multi-colored rectangle and paste them on chart paper.

3. Place the pipe cleaner in a spiral shape along with the squares so that it starts from the smallest square and spirals outwards and ends with the largest square. Attach another pipe cleaner, if needed.

4. Slide the beads into the pipe cleaner. You'll notice that the arc in each square has the number of beads corresponding to the dimensions of the square.

The Fibonacci sequence occurs naturally and has its applications in all walks of life like art, architecture, and finance. It's found everywhere from cell division to seashells and rose petals to the Milky Way galaxy. It's always nice to take note of nature's unexplained mysteries and spend a moment to wonder how it never ceases to amaze us. Happy Fibonacci Day!