Fibonacci is one of the most famous names in mathematics. This would come as a surprise to Leonardo Pisano, the mathematician we now know by that name. And he might have been equally surprised that he has been immortalised in the famous sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – rather than for what is considered his far greater mathematical achievement – helping to popularise our modern number system in the Latinspeaking world.

Have you ever pulled the petals off of a daisy? If you look closely at the center of a daisy, you will find that the yellow center is not solid. It is made up of sets of spirals that go out from the center. It’s not just daisies! Nature is all about math.
Look at the pictures of a pinecone. It has those same kinds of spirals. They don’t go around and around in a circle — they go out like fireworks. Look at the pictures below to see what that looks like. How many spirals go in the clockwise direction (green lines)? How many spirals go in a counterclockwise direction (yellow lines)? Isn’t that strange? Wouldn’t you expect that they would be the same?
To understand the spirals in pinecones, pineapples, daisies and lots of other things in nature, we have to meet a mathematician named Leonardo de Pisa. Most people call him Fibonacci (pronounced fibonawchee). About 800 years ago, he wrote a book in which he included a math problem that went like this:
“A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?”
Fibonacci’s work on this problem led him to this sequence of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …
We call this the Fibonacci sequence, and the numbers are called Fibonacci numbers. To get the next number in the sequence, you add the previous two numbers together. Now go back and look at those pinecone spirals. What do you notice about the number of spirals in each direction, now that you know about Fibonacci numbers?
Fibonacci Rectangles
We can draw rectangles using Fibonacci numbers. This will take us to an amazing place. Complete the Fibonacci sequence below (try to do it without help!):
0, 1, 1, 2, 3, 5, __ , __ , __ , __ ,
To understand the spirals in pinecones, pineapples, daisies and lots of other things in nature, we have to meet a mathematician named Leonardo de Pisa. Most people call him Fibonacci (pronounced fibonawchee). About 800 years ago, he wrote a book in which he included a math problem that went like this:
“A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?”
Fibonacci’s work on this problem led him to this sequence of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …
We call this the Fibonacci sequence, and the numbers are called Fibonacci numbers. To get the next number in the sequence, you add the previous two numbers together. Now go back and look at those pinecone spirals. What do you notice about the number of spirals in each direction, now that you know about Fibonacci numbers?
Fibonacci Rectangles
We can draw rectangles using Fibonacci numbers. This will take us to an amazing place. Complete the Fibonacci sequence below (try to do it without help!):
0, 1, 1, 2, 3, 5, __ , __ , __ , __ ,
The interesting thing about making rectangles like this is that the ratio (the number that shows how the sides relate to each other) stays the same, no matter how big the rectangle gets. This ratio gives us rectangles we call the “Golden Rectangle” because they are said to be the most beautiful rectangles to look it. The ratio is called the Golden Ratio. You can find it by dividing the long side by the short side. So if you have a rectangle that is 3 × 5, you would divide 5 by 3. This will give us a number right around 1.61

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