The Vitruvian ManThe Binomial TheoremThe Game of Poker

Vitruvian Genesis by flickr user karlequin

Expand and simplify ...

a + b

Find a pattern, add two more rows to the triangle ...

11 1

1 2 11 3 3 1

1 4 6 4 1

Evaluate each term ...n rC = n!

(n-r)!r!

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

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

Pascal's TriangleCan you find the Hockey Stick pattern?

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

1, 1, 2, 3, 5, 8, ....Fibonacci numbersCan you find them?

Bees

Bees in hive by flickr user net_efekt

Trees

Plants & Flowers

Bees and Sunflower by flickr user philcalvert

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/

The Rule Of Thirdshttp://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.