Download Homework 13/10/11 Pascal`s Triangle

Homework 13/10/11 Pascal's Triangle
One of the most interesting Number Patterns is Pascal's
Triangle (named after Blaise Pascal, a famous French
Mathematician and Philosopher).
To build the triangle, start with "1" at the top, then
continue placing numbers below it in a triangular
pattern.
Each number is just the two numbers above it added
together (except for the edges, which are all "1").
(Here I have highlighted that 1+3 = 4)
Here is a tetrahedron
(3d shape, triangular based pyramid)
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


For height=1 you only need one marble
For height=2, you would need 4 marbles (1 at the top and 3
below)
For height=3 you would need 10 marbles.
For height=4 you would need 20 marbles.
These totals are tetrahedron numbers.
The number of marbles in each layer are triangular numbers.
Patterns Within the Triangle
Look at the numbers as they follow diagonals. Write about any mathematical patterns you
notice.
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Horizontal Sums
What do you notice about the horizontal sums? Is there a pattern when the digits are added
together?
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Powers of 11
Use a calculator. Start from line 2. do the following calculations: 11 x 1, 11 x 11, 11 x 11 x 11
etc. What do you notice?
Complete this part of Pascal’s triangle: