Mathematics Pascals Triangle Date 22.10.13 James McKee.
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Transcript of Mathematics Pascals Triangle Date 22.10.13 James McKee.
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 6 4 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:
Q. 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.
Questions?