Transcript 1 - Royal Holloway

Mathematics
Pascal’s Triangle
Date 22.10.13
James McKee
Challenge overview
What is Pascal’s triangle?

1

1


 1
2
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
What is Pascal’s triangle?

What patterns can you spot?

1
1


 1
3
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?


 1
4
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

 1
5
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

 1
Joke:
Q. What does the B in Benoît B
Mandlebrot stand for?
6
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
What is Pascal’s triangle?

What patterns can you spot?

Which rows have only odd numbers?

Odd/even pattern: fractals.

 1
Joke:
Q. What does the B in Benoît B
Mandlebrot stand for?
A. Benoît B Mandelbrot
7
1
1
1
1
1
2
3
4
1
3
6
1
4
1
Challenge overview
Class experiment: coin tossing.
Come to the Science Festival to see a
Galton board.
Challenge: understand the connection
with Pascal’s triangle.
8
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.
9
Curriculum links
Number
 Spot patterns
 Use decimal numbers
 Divisibility: odd or even
10
Curriculum links
Statistics
 Design experiments
 Appreciate the concept of bias
11
Added value
Support and feedback from enthusiastic
Royal Holloway staff.
12
Added value
Support and feedback from enthusiastic
Royal Holloway staff.
Come to Super Science Saturday and
play with a Galton Board.
13
Questions?