Originally Pascal’s Triangle was developed by the Chinese of long ago. But then the French mathematician Blaise Pascal was officially the first person to discover the importance of the patterns it had within itself. But how exactly does it work??? In this research paper, I will explain how to make the Pascal’s Triangle and why it is so special. Construction:

Pascal’s Triangle is basically a triangle of numbers. “At the tip of the triangle is the number 1, which makes up row zero. Then the second row has two 1’s by adding the 2 numbers above them to the left and right, 1 and 0 (all numbers outside the triangle are zeros). Now do the same for the second row.” 0+1= 1, 1+2=3, 2+1=3, 1+0=1. Then the results become the third row. 0+1=1, 1+3=4, 3+3=6, 3+1=4, and 1+0=1. Then the pattern continues on infinitely.

￼

There seems to be many patterns in this triangle. For example: The Sums of the Rows.

The Sums of the Rows:
“The sum of the numbers in any row is equal to 2 to the nth power or 2^n when n represents the number of the row.” For example: 20 = 1
21 = 1+1 = 2
22 = 1+2+1 = 4
23 = 1+3+3+1 = 8
24 = 1+4+6+4+1 = 16

Prime Numbers:
“If the 1st element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it. For example, in row 7 (1 7 21 35 35 21 7 1) 7, 21, and 35 are all divisible by 7.”

The Hockey Stick:
“If a diagonal of numbers of any length is selected starting at any of the 1's bordering the sides of the triangle and ending on any number inside the triangle on that diagonal, the sum of the numbers inside the selection is equal to the number below the end of the selection that is not on the same diagonal itself.” Look at the example on the next page if you don’t understand. ￼

Magic 11’s:
“If a row is made into a single number by using each element as a digit of the number (carrying over when an element itself has more than one digit), the...

...Luis Puga Trig.
Ms.Candidato 2/20/12
The Pascal’s Triangle
The Pascal’s Triangle is a triangular array of the binomial coefficients. The system after French mathematician Blaise Pascal. The set of numbers that form Pascal's triangle were known before Pascal. However, Pascal developed many uses of it and was the first one to organize all the information together in his treatise, Traité du...

...comparison of FORTRAN and Pascal
By: Peter Ryan
Richard Zultak
Brendt Lozen
University Of Phoenix
Dan Cohen
POS370
Programming Concepts
Sep 12th 2007
Abstract
The following is a research paper regarding two programming languages called FORTRAN and Pascal.
Pascal [mathematician/philosopher Blaise Pascal] was designed primarily as a tool for teaching good programming skills, but - thanks largely to the...

...
Pascal Programming
Arieus Green
Professor Gary Smith
Sam Houston State University
Pascal was designed in 1968, but was no published until the 1970 by the mind of a man named Niklaus Wirth. Niklaus Wirth was born in Winterthur, Switzerland in 1934 were he attended Swiss Federal Institute of Technology Zurich. Where he soon earns his degree in Electronic Engineering by the mid 1960’s. Pascal was named based off the...

...given non - collinear points is:
[Marks:1]
A.
Two
B.
infinitely many
C.
Four
D.
Three
6]
The area of a right triangle with base 5 m and altitude 12 m is
[Marks:1]
A.
50 m2
B.
15 m2
C.
9 m2
D.
30 m2
7]
Evaluate: 53 - 23 - 33
[Marks:1]
A.
80
B.
60
C.
120
D.
90
8]
The area of an equilateral triangle of side 14 cm is
[Marks:1]
A.
B.
C.
D.
9]
Simplify:
[Marks:2]...

...
5C Problems involving triangles
cQ1. The diagram shows a sector AOB of a circle of radius 15 cm
and centre O.
The angle at the centre of the circle is 115.
Calculate (a) the area of the sector AOB.
(b) the area of the shaded region. (226 , 124
nQ2. Consider a triangle and two arcs of circles.
The triangle ABC is a right-angled isosceles
triangle, with AB = AC = 2.
The point P is...

...Pascal's triangle is a geometric arrangement of the binomial coefficients in a triangle.It is also known as the figurate triangle, the combinatorial triangle, and the binomial triangle. Even though Pascal’s Triangle is named after seventeenth century mathematician, Blaise Pascal, several other mathematicians knew about and applied their knowledge of the triangle hundreds of years before the...

...an invaluable and important concept in fluid mechanics and its applications especially in the automotive industry, mechanical engineering, and hydraulics.
Pascal's law or the principle of transmission of fluid-pressure that was proposed by Blaise Pascal. According to Bloomfield, the law is a principle in fluid mechanics that states that for a particular position within a fluid at rest, the pressure is the same in all directions.
Pascal's principle is defined as
A change in...

...Blaise Pascal
“There are two types of minds - the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the dive.” From childhood he was a scientific prodigy. Just from this quote of his you can tell that even his mind in itself can fathom things that none of us even think about on a daily basis. Blaise Pascal...