2. Explaining Why I Choose That Topic
Initially, I was not sure about that topic because
I have the possibility of limited options before I
preapring this homework.And then, this topic
entered my mind.I started to research how I
preapre the good homework.It looks like
interesting and special topic for me.
3. PASCAL’S
TRIANGLE
We learn this subject at 8th
grade.Let’s remember:
Blaise Pascal, (a famous
French Mathematician and
Philosopher) can found this
type of special triangle.
Each number in the triangle is
the sum of the two directly
above it.
4. Patterns Within the Triangle
DIAGONALS
The second diagonal numbers
are the Counting
Numbers (1,2,3, etc).
The third diagonal has
the triangular numbers
(The fourth diagonal, not
highlighted, has the
tetrahedral numbers.)
5.
6. ODDS AND EVENS
If we color the Odd
numbers, we can
easily see the same as
the Sierpinski Triangle
7.
8. Horizontal Sums
What do you know
about the horizontal
sums?
Isn't it amazing! It
doubles each time
(powers of 2).
9. Exponents of 11
Each line is also the
exponents of 11:
110=1 (the first line is just a
"1")
111=11 (the second line is
"1" and "1")
112=121 (the third line is
"1", "2", "1")
10. Squares
For the second diagonal, the
square of a number is equal
to the sum of the numbers
next to it and below both of
those.
Examples:
32 = 3 + 6 = 9,
42 = 6 + 10 = 16,
52 = 10 + 15 = 25,
11. Fibonacci Sequence
If we can collect
which number we
can examine and
this numbers
upper right
diagonals numbers,
we can see the
Fibonacci sequence
13. Using Pascal’s Triangle
Heads and Tails
If we can toss a coin, we have
2 posibilities. (H-T)
And if we can toss the two
coins, we have the 4
posibilities. (HH – HT – TH –
TT) etc…
THIS POSIBILITIES ARE SHOWS
US THE PASCAL’S TRIANGLE.