So, what do sunflowers have to do with math?
It has to do with the number of seeds which are arranged in the center and their connection to the Fibonacci Sequence!
The Fibonacci Sequence is a sequence which begins with 1 and in which every term thereafter is the sum of the two preceding terms:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
One of the interesting things about the numbers in this sequence is that they appear throughout nature.
If you start with a pair of rabbits and breed them, they will produce one pair of offspring after one month and a second pair of offspring after the second month. If they stop breeding, each new pair of rabbits will produce two more pairs of offspring in the same way, and so on. We represent the original pair of rabbits with the number 1. After one month, they produce 1 new pair of rabbits - also represented by the number 1. But the following month, since both pairs of rabbits reproduced, we have 2 new pairs of offspring in the third month - represented by the number 2. Each number represents a new generation of rabbits. The next (or 4th) generation will produce 3 pairs of offspring. The interesting thing about this breeding pattern is that each generation of rabbits produces pairs of offspring equal to the sum of the previous two numbers - or Fibonacci numbers!
Ratios of Fibonacci numbers are related to plant growth as well. When new leaves grow from the stem of a plant, they grow upward in a spiral around the stem. The amount of turning from one leaf to the next is a fraction of a complete rotation around the stem - and the numerator and denominator of the fraction are always Fibonacci numbers! For example, if you look at any particular leaf on such a plant, then look for a leaf directly above it, there will be turns and spaces between these - and the numbers will be Fibonacci numbers! For example, there could be 5 complete turns and 8 spaces. Nature spaces the leaves this way so that the leaves higher up on the plant are far enough way so as not to block the sunlight from the leaves lower on the plant.
On many plants, their number of petals is a Fibonacci number: For example, lilies and irises have 3 petals, marigolds have 13 petals, and daisies can have 34, 55 or even 89 petals. Fibonacci numbers are also present in the arrangement of seeds on flower heads, where the petals form spirals curving in different directions. On a sunflower, the number of spirals curving in one direction from the center is 34. Closer to the edge of the sunflower, there are 55 spirals curving one way and 89 curivng in the opposite direction - all Fibonacci numbers! (So, that's what sunflowers have to do with math!)
If you take the ratio of successive terms of the Fibonacci sequence, this ratio approaches a value called the golden mean or golden ratio. This value is approximately 1.6 and is represented by the Greek letter, phi (φ ). The further out in the sequence you go, the closer the ratio is to phi.
The golden ratio is also present in art and architecture. It has been said that a rectangle that is most pleasing to the eye has a width and length which are in the golden ratio. Even in early Greek civilization, their buildings were often constructed using "golden rectangles".
You can read more about this intriguing sequence (and see some great pictures) by going to the link below:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
It has to do with the number of seeds which are arranged in the center and their connection to the Fibonacci Sequence!
The Fibonacci Sequence is a sequence which begins with 1 and in which every term thereafter is the sum of the two preceding terms:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .
One of the interesting things about the numbers in this sequence is that they appear throughout nature.
If you start with a pair of rabbits and breed them, they will produce one pair of offspring after one month and a second pair of offspring after the second month. If they stop breeding, each new pair of rabbits will produce two more pairs of offspring in the same way, and so on. We represent the original pair of rabbits with the number 1. After one month, they produce 1 new pair of rabbits - also represented by the number 1. But the following month, since both pairs of rabbits reproduced, we have 2 new pairs of offspring in the third month - represented by the number 2. Each number represents a new generation of rabbits. The next (or 4th) generation will produce 3 pairs of offspring. The interesting thing about this breeding pattern is that each generation of rabbits produces pairs of offspring equal to the sum of the previous two numbers - or Fibonacci numbers!
Ratios of Fibonacci numbers are related to plant growth as well. When new leaves grow from the stem of a plant, they grow upward in a spiral around the stem. The amount of turning from one leaf to the next is a fraction of a complete rotation around the stem - and the numerator and denominator of the fraction are always Fibonacci numbers! For example, if you look at any particular leaf on such a plant, then look for a leaf directly above it, there will be turns and spaces between these - and the numbers will be Fibonacci numbers! For example, there could be 5 complete turns and 8 spaces. Nature spaces the leaves this way so that the leaves higher up on the plant are far enough way so as not to block the sunlight from the leaves lower on the plant.
On many plants, their number of petals is a Fibonacci number: For example, lilies and irises have 3 petals, marigolds have 13 petals, and daisies can have 34, 55 or even 89 petals. Fibonacci numbers are also present in the arrangement of seeds on flower heads, where the petals form spirals curving in different directions. On a sunflower, the number of spirals curving in one direction from the center is 34. Closer to the edge of the sunflower, there are 55 spirals curving one way and 89 curivng in the opposite direction - all Fibonacci numbers! (So, that's what sunflowers have to do with math!)
If you take the ratio of successive terms of the Fibonacci sequence, this ratio approaches a value called the golden mean or golden ratio. This value is approximately 1.6 and is represented by the Greek letter, phi (φ ). The further out in the sequence you go, the closer the ratio is to phi.
The golden ratio is also present in art and architecture. It has been said that a rectangle that is most pleasing to the eye has a width and length which are in the golden ratio. Even in early Greek civilization, their buildings were often constructed using "golden rectangles".
You can read more about this intriguing sequence (and see some great pictures) by going to the link below:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html
Other Good Math Sites for More Interesting Stuff!
http://mathforum.org/
http://mathworld.wolfram.com/
http://www.coolmath.com/
http://www.khanacademy.org/ (lots of videos and examples on almost every topic imaginable!)
http://mathforum.org/
http://mathworld.wolfram.com/
http://www.coolmath.com/
http://www.khanacademy.org/ (lots of videos and examples on almost every topic imaginable!)