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Exploring Pascal's Triangle: Patterns, Experiments, and Coin Tossing Challenges

Join renowned mathematician James McKee on a journey into the fascinating world of Pascal's Triangle. In this challenge, we explore the unique patterns found within the triangle, such as odd and even rows, and their relationships to fractals. Participate in class experiments, including biased coin tossing and see the connection to Pascal's Triangle through engaging Galton boards. This interactive session promises to enhance your understanding of number patterns and statistics, supported by enthusiastic staff from Royal Holloway. Don't miss this opportunity to dive deep into mathematics!

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Exploring Pascal's Triangle: Patterns, Experiments, and Coin Tossing Challenges

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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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