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Pre-Cal 40S May 11, 2009
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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.

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

Published in: Education, Technology

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  • 1. The Vitruvian Man The Binomial Theorem The Game of Poker Vitruvian Genesis by flickr user karlequin
  • 2. Expand and simplify ... a+b
  • 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. Evaluate each term ... n! nC r = (n-r)!r!
  • 5. Pascal's Triangle How many different patterns can you find in the triangle?
  • 6. Pascal's Triangle How many different patterns can you find in the triangle?
  • 7. Pascal's Triangle Can you find the Hockey Stick pattern?
  • 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. Bees Bees in hive by flickr user net_efekt
  • 10. Trees
  • 11. Plants & Flowers Bees and Sunflower by flickr user philcalvert
  • 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. The Rule Of Thirds http://www.morguefile.com/docs/Jodie_Coston:_Lesson_1
  • 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. 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.