Welcome to the Greenery Land.

Tuesday, 2 August 2011

http://www.youtube.com/watch?v=ktLcSH4UkpE

10:12

Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

Rabbit Problem

Fibonacci’s work discussed a “rabbit problem,” which asked, "How many pairs of rabbits will there be after a year if it is assumed that every month each pair produces one new pair, which begins to bear young two months after its own

birth?”
--> The solution to this problem made the equence famous.

The Fibonacci sequence can also be found in nature.

A Bee’s Genealogy

• A drone, or male bee – hatches from an unfertilized egg. A female bee – hatches from an egg that has been fertilized. When finding the ancestry of a male bee, we observe that the Fibonacci sequence is formed.

A Pineapple’s Scales

• 3, 5, 8, 13, and even 21spirals can be found according to size. Consecutive sets of spirals run opposite of each other. (i.e., 5 would run opposite of 8).

• The higher the number of spirals, the steeper that spiral will be. Thus, no spirals moving opposite of each other will have the same spiral.

A Coneflower’s Spiraling Seeds

The seeds in the coneflower above form 34 spiraling to the left (green) and 55 spirals going

to the right (blue).

A Pinecone’s Spiraling Bracts

The bracts on the pinecone above form 8 spirals going to the right (green) and 13 spiraling to the left (yellow).

10:09

Female bees can reproduce with or without a male!

-Unfertilized, female bees bear male bees as offspring.

-Fertilized by a male bee they give birth to a female!

Following the rules above, we can see that a male bee, M was the product of an unfertilized female, F!

Now, trace the origins of this female, his mother.

Females need to come from fertalized females, so she had a mother AND a father, two parents.

Tracing their roots, the male had a single female mother, the female had a mother and a father. That's three bees.

The previous generation has five bees!

Following the progression, how many bees will be in the previous generation? If you said eight, you either found the five females and three males that make up this group, or you noticed that each unfolding level represents the next step of the Fibonacci Sequence!

09:54