# Fun with Pascal's Triangle

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Create any “hockey stick”
pattern, starting at a one
on the edge moving
diagonally down, then
change direction at the
end for the last space.

will always be double the
last number.

Try a couple of your own.

Pascal’s Triangle                     Row each row into a calculate:
single number 11ROW=
0           1          110 = 1
1          11          111 = 11
2         121         112 = 121
3        1331
4        14641
5       161051
6      1771561
7      19487171
8     214358881
9    __________
10   __________

If your numbers were 1 5 10 10 5 1, then combine them like so:
100000
50000
10000
1000
50
1
----------
161051
Part A:
Draw 3 points, evenly spaced, on the circle below and determine:

How many different line segments can be
formed from connecting the dots?

How many triangles visible when all the
dots are connected to all the other dots?

How many quadrilaterals do you see?

Part B:
Draw 4 points, evenly spaced, on the circle below and determine:

How many different line segments can be
formed from connecting the dots?

How many triangles visible when all the
dots are connected to all the other dots?

How many quadrilaterals do you see?

Number of    Lines Formed Triangles         Quadrilaterals   Pentagons
Dots                      Formed            Formed
1             0            0                 0                0
2             1            0                 0                0
3                                            0                0
4                                                             0
5                                                             1
6
Reading the rows diagonally, you would see this pattern.

1
2        1
3        3          1
4        6          4           1
5        10         10          5           1
6        15         20          15          6          1
7        21         35          35          21         7       1
Points on a Circle
Image   Points Segments Triangles Quadrilaterals Pentagons Hexagons Heptagons

1

2       1

3       3        1

4       6        4           1

5      10        10          5           1

6      15        20         15           6         1

7      21        35         35          21         7         1
Even the Fibonacci Sequence appears in Pascal’s Triangle

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 views: 4 posted: 12/4/2011 language: English pages: 5