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 birth of Pascal in 1623. The Arabs, Persians and the Chinese discovered Pascal’s triangle in earlier centuries. The earliest depictions of a triangle of binomial coefficients occur in the tenth century in commentaries on the Chandas Shastra. The Chandas Shastra was an ancient Indian book on Sanskrit prosody written by Pingala between the fifth and second centuries BC. Though Pingala's work was found in fragments, Halayudha, around 975, used the triangle to explain obscure references to Meru-prastaara, the "Staircase of Mount Meru". It was also realised that the shallow diagonals of the triangle were sums to the Fibonacci numbers. The Indian mathematician Bhattotpala later gave rows 0-16 of the triangle. Around the same time, the traingle was discussed by mathematicians in Persia, Al-Karaji,and mathematician Omar Khayyám, reffered to the traingle as the "Khayyam triangle" in Iran. Many theorems related to the triangle were known, including the binomial theorem. In fact Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients. Chinese mathematician Chia Hsien showed that he was using the triangle to extract square and cube roots of numbers. In China, after Chia Hsien’s discovery of the relationship between extracting roots and the binomial coefficients of the triangle, work continued on this topic by several Chinese algebraists to solve higher than cubic equations. In 13th century, Yang Hui presented the arithmetic triangle, which was the same as Pascal's Triangle. Today Pascal's triangle in China is reffered...

...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...

...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...

...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...

...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...

...frequency for something to happen. Blaise Pascal is referred to as the father of probability. Pascal contributed to the branch of mathematics known as probability in 1653. Through his work in probability, Pascal invented the binomial coefficients which are now known as Pascal’s Triangle. Pascal’s major input to the philosophy of mathematics came with his “Of the Geometric Spirit””.1 Blaise Pascal was also a major...

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