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Transcript

PASCAL'S TRIANGLE

$1.25

Journalist - Josue Concepcion

Vol. 1 Mr. Galvin XVIII Prd. 4

This Triangle concept has been around...

FOR A VERY LONG TIME

" I BORROWED IT " - Blaise Pascal

History

MORE ON BLAISE PASCAL

  • He lived from 1623 -1662
  • Was a French philosopher and scientist and of course was one of the most influential mathematicians ever.
  • He also was an expert in hydrostatics, a religious philosopher and as well as an inventor.
  • This man basically did everything at this time period.
  • Created an early computing machine.
  • The Pascal (Pa) which is a unit of pressure was named after him

Hidden Patterns

More than meets the eye

Fibonacci's Sequence

Pascals triangle was not actually created by Blaise Pascal himself because originally in Asia this triangle was seen in the thirteenth century unlike Pascals which was in the seventeenth. Yang Hui's triangle had the same triangle and was appropriately named after him in China. Hui was also one of the first humans to describe the properties of the triangle.

But even before Yang Hui the triangle of numbers was traced to be described by the mathematician Omar Khayyam in (1044-1123) but even before that Halayudha in 975!

The sum of the numbers in the consecutive rows are the first numbers in the Fibonacci Sequence. It's formed by adding two consecutive numbers in the order to produce the next number.

In real life the Fibonnacci Sequence can be found in the length of the segments of a pentagram, and in nature and how things grow in as well as the curve found in a string instrument. Example 1,1,2,3,45,8,13,21,34,55,89,144,233....

Found : http://www.cut-the-knot.org/arithmetic/combinatorics/PascalTriangleProperties.shtml

Hidden Patterns

More than meets the eye

Sierpinski's Triangle

FIBONACCI CONTINUED...

Fibonacci's Sequence

There is a link between Pascal's triangle and Sierpinski's Triangle. When all of the odd numbers in Pascal's Triangle are shaded in and all of the evens are left, the expanding and recursive Sierpinski Triangle is shown.

EXAMPLES

FOUND IN REAL LIFE

Found: http://ptri1.tripod.com/

The Fibonacci Sequence is actually found in multiple places in nature. Some of the things found in nature can actually be seen, such as in shells, in trees, and in the exponential growth of flower petals. Even the seed pods on a pine cone are in a pattern of the Fibonacci sequence.

MY NEW TRIANGLE

MULTIPLY BY FIRST TERM

RULES:

1. Count which line you are on.

2. Make that your first number

then proceed to multiply

the normal pascals

triangle line by that

first number.

1

2 2

3 6 3

4 12 12 4

5 20 30 20 5

6 30 60 60 30 6

7 42 105 140 105 42 7

8 56 168 280 280 168 56 8

9 81 324 756 1134 1134 756 324 81 9

10 100 450 1200 2100 2520 2100 1200 450 100 10

If you take the first number and divide by the second you get the first number

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