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Mathematics Pascal’s Triangle

Mathematics Pascal’s Triangle. Date 22.10.13 James McKee. Challenge overview. What is Pascal’s triangle?. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1. Challenge overview. What is Pascal’s triangle?

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Mathematics Pascal’s Triangle

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  1. MathematicsPascal’s Triangle Date 22.10.13 James McKee

  2. Challenge overview • What is Pascal’s triangle? • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 6 4 1

  3. Challenge overview • What is Pascal’s triangle? • What patterns can you spot? • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 64 1

  4. Challenge overview • What is Pascal’s triangle? • What patterns can you spot? • Which rows have only odd numbers? • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 6 4 1

  5. Challenge overview • What is Pascal’s triangle? • What patterns can you spot? • Which rows have only odd numbers? • Odd/even pattern: fractals. • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 6 4 1

  6. Challenge overview • What is Pascal’s triangle? • What patterns can you spot? • Which rows have only odd numbers? • Odd/even pattern: fractals. • Joke: • Q. What does the B in Benoît B Mandlebrot stand for? • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 6 4 1

  7. Challenge overview • What is Pascal’s triangle? • What patterns can you spot? • Which rows have only odd numbers? • Odd/even pattern: fractals. • Joke: • What does the B in Benoît B Mandlebrot stand for? • A. Benoît B Mandelbrot • 1 • 1 1 • 1 2 1 • 1 3 3 1 • 1 4 6 4 1

  8. Challenge overview • Class experiment: coin tossing. • Come to the Science Festival to see a Galton board. • Challenge: understand the connection with Pascal’s triangle.

  9. Challenge overview • Class experiment: biased coin tossing. • Is the first digit after the decimal point of sin(n) even or odd? • Challenge: understand the connection with Pascal’s triangle.

  10. Curriculum links • Number • Spot patterns • Use decimal numbers • Divisibility: odd or even

  11. Curriculum links • Statistics • Design experiments • Appreciate the concept of bias

  12. Added value • Support and feedback from enthusiastic Royal Holloway staff.

  13. Added value • Support and feedback from enthusiastic Royal Holloway staff. • Come to Super Science Saturday and play with a Galton Board.

  14. Questions?

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