Pascal's Triangle
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Pascal's Triangle

 

Pascal's triangle was first introduced by the Chinese mathematician Yang Hui, but it got it's name from Blaise Pascal who 500 years later rediscovered it along with Omar Khayyam.

The triangle is used to look for the probability of any particular event to occur. There are many other things that can be found in the triangle. Listed below are a few of them and how to achieve them.

PASCAL'S TRIANGLE
How to make Pascal's Triangle. Row 0 is the first row, it will have a 1. Row 1 is actually the second row it will have 1 and 1, but not to be confused with 11. The next row is the numbers 1 and 2 and 1. Now how did we get these numbers? 1 is ALWAYS going to be the first number in the row, but in order to make the triangle grow you add the two numbers above. Example: 1 + 2 = 3 and 2 + 1 = 3, so for the next line we will have 1 (always on the outside) and 3 and 3 and then 1 again. The next line gets even bigger, 1 (outside again) 1 + 3 = 4, and 3 + 3 = 6, and 3 + 1 = 4, and then that 1 again.

This can go on as long as anyone wants it to go.

POWER OF 11
The first 5 powers of 11 are in the top of the triangle. 110 = 1, 111 = 11, 112 = 121, 113 = 1331, and 114 = 14641. When these numbers are stacked in a pyramid it will form the top part of the triangle.

ADDITION ANSWERS
If you start at any given 1 and go diagonally down and then make a one step left you will find the answer to the numbers that you just followed. For example: 1 + 2 + 3 + 4 + 5 = 15, or try any other number 1 + 8 + 36 + 120 + 330 = 495.

SQUARED
Take any number next to one and make a triangle with the number directly beside it and the one below the two, when this number is squared you will have the answer of the two additional numbers when they are added together. For example: 52 = 25, looking to the right of 5 is 10, now look at the number below the 5 and 10, should be 15, now 10 + 15 = 25.

ADD THE ROWS
Any row starting with a 1 can be added straight across to find the sum of 2 to the power of that rows number. Example: 20 = 1, 21 = the addition of the next row (1 + 1) = 2, 22 = (1 + 2 + 1) = 4, 23 = (1 + 3 + 3 + 1) = 8, what about the 10th row? 1 + 9 + 36 + 84 + 126 + 126 + 84 + 36 + 9 + 1 = 512, which is 29. WOW!! Is this fun....

FIBONACCI NUMBERS
The sum of the numbers in a diagonal line downward are the first numbers of the Fibonnacci Sequence. Example: 1 is alone so = 1, then the next would also be 1 = to 1, then 1 and 1 = 2, 2 and 1 = 3, 1 and 3 and 1 = 5, 3 and 4 and 1 = 8, 1 and 6 and 5 and 1 = 13, this can be done all the way down the triangle (as the triangle gets bigger it gets a little confusing, so make sure you color out the numbers you have already used). Now take the = numbers like this: 1 + 1= the next number 2. 1 + 2 = the next number 3, 2+3 = the next number 5, 3 + 5 = the next number 8, so forth and so on. By the way Fibonacci's sequence were used to discribe a curve found in many string instruments.

Contributed by Cris Edelman

References:

  1. Pascal's Triangle
  2. All You Ever Wanted to Know About Pascal's Triangle and more.
  3. Pascal's Traingle

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