SUBMITTED BY- PRACHI GOYAL IT 2nd YEAR PASCAL’S TRIANGLE SUBMITTED BY- PRACHI GOYAL IT 2nd YEAR

HISTORY OF PASCAL’S TRIANGLE Although 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.

HOW TO CONSTRUCT IT

Another way construct it is C(n,r)=n!/r!*(n-r)!

Properties of Pascal’s triangle 1 Properties of Pascal’s triangle 1.Sum of all elements in a row is 2^n,where n is the row number.

2.Each number in a row corresponds to 11^n ,where n is the row number.

3.Counting numbers. Moving along the first diagonal , we get the counting numbers.

4.Triangular numbers and square numbers.

Proof of : 1.C(n,r)=C(n,n-r) Due to symmetry. 2.C(n,r)=C(n-1,r)+C(n-1,r-1) Clearly observed in triangle

Images Points Line-Segments Triangles Quadrilaterals Pentagons Hexagons Heptagons 1 2 3 4 6 5 10

6.Hockey stick pattern

7.Fibonacci series

8.Square pattern

9.Hexagonal property: 4*10*15=5*6*20

This was all about Pascals’s triangle Thank-You