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Pre-Cal 40S May 11, 2009

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Pascal's Triangle, the Fibonacci sequence, The Golden Ratio, The Binomial Theorem.

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Pre-Cal 40S May 11, 2009

1. 1. The Vitruvian Man The Binomial Theorem The Game of Poker Vitruvian Genesis by ﬂickr user karlequin
2. 2. Expand and simplify ... a+b
3. 3. Find a pattern, add two more rows to the triangle ... 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1
4. 4. Evaluate each term ... n! nC r = (n-r)!r!
5. 5. Pascal's Triangle How many different patterns can you ﬁnd in the triangle?
6. 6. Pascal's Triangle How many different patterns can you ﬁnd in the triangle?
7. 7. Pascal's Triangle Can you ﬁnd the Hockey Stick pattern?
8. 8. Pascal's Triangle How many different patterns can you ﬁnd in the triangle? 1, 1, 2, 3, 5, 8, .... Fibonacci numbers Can you ﬁnd them?
9. 9. Bees Bees in hive by ﬂickr user net_efekt
10. 10. Trees
11. 11. Plants & Flowers Bees and Sunﬂower by ﬂickr user philcalvert
12. 12. The Golden Ratio 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... (one quot;hquot; of a lot cooler than π) http://goldennumber.net/
13. 13. The Rule Of Thirds http://www.morgueﬁle.com/docs/Jodie_Coston:_Lesson_1
14. 14. The Binomial Theorem ... Algebraically Combinatorically Notice the patterns ... (1) The coefﬁcient of the term is: (2) The exponent on a is given by: [n - (i - 1)] (3) The exponent on b is given by: i - 1 (4) This relation holds for each term in the expansion: [exponent on a] + [exponent on b] = n (5) The number of terms in any binomial expansion is: n + 1
15. 15. Tomorrow we'll have a workshop class and we'll talk a little bit about poker. Wednesday will be a pre-test, and the test will be on Thursday.