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Das Pascalsche Dreieck

Das Pascalsche Dreieck. Blaise Pascal. Das Pascalsche Dreieck. 1653. 1623 - 1662. 1. 1. 1. 2. 1. 1. 1. 3. 3. 1. 1. 4. 6. 4. 1. 1. 5. 10. 10. 5. 1. 6. 1. 15. 20. 15. 6. 1. 1. 7. 21. 35. 35. 21. 7. 1. 1. 8. 28. 56. 70. 56. 28. 8. 1. 1. 9. 36.

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Das Pascalsche Dreieck

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  1. Das Pascalsche Dreieck

  2. Blaise Pascal Das Pascalsche Dreieck 1653 1623 - 1662

  3. 1 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  4. 1 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  5. 1 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  6. Nur 1’sen. Summiere auf: 1 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  7. 1 Natürliche Zahlen 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  8. 1 Natürliche Zahlen. Summiere auf: 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  9. 1 1 1 Dreieckszahlen 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  10. 1 1 1 2 1 1 Tetraeder Zahlen 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  11. 1 Hockey Schläger 1 1 2 1 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  12. Zeilensummen 1 0 1 2 1 1 1 4 2 2 1 1 8 3 1 3 3 1 16 1 4 6 4 1 32 1 5 10 10 5 1 64 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 Beweis? 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  13. Potenzen von (a+b) 1 a+b a2+2ab+1b2 0 1 1 1 1 2 2 1 1 3 1 3 3 1 a3 +3 a2 b+3ab2+1b3 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 Beweis? 1 10 45 120 210 252 210 120 45 10 1

  14. Potenzen von (1+x) 1 1+x 1+2x+1x2 0 1 1 1 1 2 2 1 1 3 1 3 3 1 1+3x+3x2+1x3 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 Beweis? 1 10 45 120 210 252 210 120 45 10 1

  15. Potenzen von 11 1 11 121 0 1 1 1 1 2 2 1 1 3 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  16. 0 Koordinatensystem n 1 0 1 2 c(n,k) 1 1 1 3 c(n+1,k) = c(n,k) + c(n,k-1) 2 1 1 2 4 c(n,0) = 1 1 3 3 1 3 c(n,n) = 1 5 1 4 6 4 1 4 k 1 5 10 10 5 1 5 6 1 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1

  17. 1

  18. 1 + 2 = 3

  19. 3 + 3 = 6

  20. 6 + 4 = 10

  21. 10 + 5 = 15

  22. 15 + 6 = 21

  23. 1

  24. 1 + 3 = 4

  25. 4 + 6 = 10

  26. 10 + 10 = 20

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