Pascal's Triangle

MATHEMATIC PERFORMANCE WORK

Name-Surname: Mehmet EROĞLUNumber-Class: 9-I 591Performance Work’s Subject: PASCAL’S TRIANGLE

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.

PASCAL’S TRIANGLEWe 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.

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.)

ODDS AND EVENS

If we color the Odd numbers, we can easily see the same as the Sierpinski Triangle

Horizontal Sums

What do you know about the horizontal sums?Isn't it amazing! It doubles each time (powers of 2).

Exponents of 11Each 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")

SquaresFor 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,

Fibonacci Sequence

If we can collect which number we can examine and this numbers upper right diagonals numbers, we can see the Fibonacci sequence

Symetrical

The numbers on the left side have identical matching numbers on the right side.

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.