Pre-Cal 40S May 11, 2009

The Vitruvian Man The Binomial Theorem The Game of Poker Vitruvian Genesis by ﬂickr user karlequin

Expand and simplify ... a+b

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

Evaluate each term ... n! nC r = (n-r)!r!

Pascal's Triangle How many different patterns can you ﬁnd in the triangle?

Pascal's Triangle Can you ﬁnd the Hockey Stick pattern?

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?

Bees Bees in hive by ﬂickr user net_efekt

Trees

Plants & Flowers Bees and Sunﬂower by ﬂickr user philcalvert

The Golden Ratio 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... (one \"h\" of a lot cooler than π) http://goldennumber.net/

The Rule Of Thirds http://www.morgueﬁle.com/docs/Jodie_Coston:_Lesson_1

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

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.

Pre-Cal 40S May 11, 2009

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Notes on slide 1

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