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Our Project Blog:D
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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


1. What is the probability of guessing this combination lock?

-Four digit combination.
-Numbers range from 0 to 9.
-The possible numbers are from 0000 to 9999, so that's 1 in 10000. I.e., very unlikely with one go at it and it'd take them a while to try every combination.
 

2. Whats the odds of getting a multiple response question correct, when the answer can be a combination of 4?

-There are 4 choices
-Correct answer can be any one, all four, or any combination of 2 or 3
-Possible compinations: a, ab, ac, ad, abc, abd, acd, b, bc, bd, bcd, c, cd, d, abcd
= 15 combinations

07:35


1.  Combinations without Repetition
This is how lotteries work. The numbers are drawn one at a time, and if you have the correct numbers (no matter what order) you win!
Using a pool ball example, let us say that you just want to know which 3 pool balls were chosen, not the order. We already know that 3 out of 16 gave us 3,360 permutations.
Pascal's Triangle
You can also use Pascal's Triangle to find the values. Go down to row "n" (the top row is 0), and then along "r" places and the value there is your answer. Here is an extract showing row 16:

1    14    91    364  ...
1    15    105   455   1365  ...
1    16   120   560   1820  4368  ...
http://www.mathsisfun.com/combinatorics/combinations-permutations.html

i dont really understand this but may be you will so read and see tmr we can discuss

00:40


The pascal's triangle can be used to:
-calculate probability
-find binomial expansion coefficients
-find singular, triangular and tetrahedral numbers
-find exponents of 11
-find the Fibonacci sequence


So I guess we can just come up with daily problems with regards to these applications and tadaa we have an application (:

http://www.mathsisfun.com/pascals-triangle.html

00:39