Patterns, Patterns, and more Patterns!

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Presentation transcript:

Patterns, Patterns, and more Patterns! Pascal’s Triangle Patterns, Patterns, and more Patterns!

It all starts with 1 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

And continues with the counting numbers (the Naturals) 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 And continues with the counting numbers (the Naturals)

… and the Triangular Numbers 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 … and the Triangular Numbers

Rows add to powers of 2 4 1 3 2 6 7 5 9 8 1 = 2 = 4 = 22 8 = 23 16= 24 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 1 = 2 = 4 = 22 8 = 23 16= 24 32= 25 64= 26 128= 27

28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 Even Numbers

Numbers Divisible by 3 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

Numbers Divisible by 5 28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

Numbers Divisible by 6 28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 Numbers Divisible by 7

And so it goes, on, and on, and on …