1 / 11

Exploring

Exploring. What is Pascal’s Triangle?. It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it. Building Pascal’s Triangle.

kolina
Télécharger la présentation

Exploring

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Exploring

  2. What is Pascal’s Triangle? • It’s a triangle. • A triangle of numbers! • Pascal did not create it…. The Chinese did. • Blaise Pascal discovered all of the unique patterns in it.

  3. Building Pascal’s Triangle You can keep adding rows until the cows come or your hand hurts or your run out of paper! 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 Then we add the left and right number together on the second row Continue with this addition for each line First we start off with a triangle of ones

  4. 20 Row Pascal’s Triangle Just imagine 40 rows of a Triangle!

  5. A Closer Look at Rows The very top is Row 0 Each row has a reference number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 The sum of all the numbers in a row = 2Row Number What is the sum of the eighth row? The sum of row 6 = 26 or 64 The answer is 28 or 256

  6. Let’s Look at Elements The first element is always element zero All of these 1’s are element 0 The next number in each row would be element 1 Each number or element in a row has a reference number starting with the number 1. Let’s look at the 6th row! Element 1 Element 3 Element 5 Element 0 Element 2 Element 4 Element 6

  7. Find the Elements We’re at the 6th row Now let’s go to the 3rd element 2 0 1 3 Let’s find the 3rd element in 6th row

  8. Find an Element Using Math Here is the 3rd element in 6th row 2 1 3 5! = 5×4×3×2×1 or 120 10! = 10×9×8×7×6×5×4×3×2×1 or 3,628,800 “!” is a factorial. Start with the number and multiply by every sequential number down to 1 Find 6C3 (nCr) or the 6th row choose 3rd element n! 6×5×4×3×2×1 720 720 720 _______ _______ _____ _____ _____ = 20 r!(n-r)! 3×2×1(6-3)! 6(3)! 6(3×2×1) 36

  9. Theory into Practice • Let’s find the 5 element in the 15th row • We are finding nCr or 15C5. • We are using our formula with n being the row and r being the element. n! _______ nCr = r!(n-r)! 3003 15! 1307674368000 _______ Crunch _______ 5C15 = 5!(15-5)! 120(3628800)

  10. Test Your Answer Go to the 15th row Now over to where the 5th element would be 3003 Add together the two number above the 5th spot.

  11. Other Interesting Facts

More Related