Download - Pre-Cal 40S May 11, 2009
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The Vitruvian ManThe Binomial TheoremThe Game of Poker
Vitruvian Genesis by flickr user karlequin
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Expand and simplify ...
a + b
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Find a pattern, add two more rows to the triangle ...
11 1
1 2 11 3 3 1
1 4 6 4 1
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Evaluate each term ...n rC = n!
(n-r)!r!
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Pascal's TriangleHow many different patterns can you find in the triangle?
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Pascal's TriangleHow many different patterns can you find in the triangle?
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Pascal's TriangleCan you find the Hockey Stick pattern?
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Pascal's TriangleHow many different patterns can you find in the triangle?
1, 1, 2, 3, 5, 8, ....Fibonacci numbersCan you find them?
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Bees
Bees in hive by flickr user net_efekt
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Trees
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Plants & Flowers
Bees and Sunflower by flickr user philcalvert
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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...The Golden Ratio (one "h" of a lot cooler than π) http://goldennumber.net/
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The Rule Of Thirdshttp://www.morguefile.com/docs/Jodie_Coston:_Lesson_1
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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
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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.