PASCALS TRIANGLE s Blaise Pascal pronounced blz paskal

PASCAL’S TRIANGLE

s Blaise Pascal (pronounced [blɛz paskal]), (June 19, 1623 – August 19, 1662) was a French mathematician, physicist, and religious philosopher. He was a child prodigy who was educated by his father. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the construction of mechanical calculators. s Pascal was a mathematician of the first order. He helped create two major new areas of research. He wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

Blaise Pascal s s It is not known whether Pascal’s triangle was an original work. What is known is that mathematicians from Persia, India, China, and France have all experimented with creating triangular arrangements of numbers. The earliest known number triangle was made in 1070 by the Persian, Omar Khayyam. A Chinese version was published in 1303 by Chu Shih-Chieh. The first printed European version dates back to 1527. In 1654, Blaise Pascal worked with Pierre Fermat to discover how patterns in the arithmetic triangle related to chances in gambling. This research became the foundation of probability theory. The patterns he discovered in this triangle have fascinated mathematicians for hundreds of years.

s To keep the numbers in Pascal’s triangle organized, we use hexagonal cells. To begin the triangle, start it with the number one in the top cell. After the initial “seed” of one, the rule is to add the two numbers diagonally above a cell to produce the number for that cell. If there is no cell above on the right or left, consider the missing cell to be a zero. The first four rows will look like this:

NOW IT’S YOUR TURN! s COMPLETE THE FIRST 9 ROWS

s In terms of odd and even, what are the outcomes as you continue this pattern?