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

2. 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.

3. HOW TO CONSTRUCT IT

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

5. 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.

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

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

8. 4.Triangular numbers and square numbers.

9. 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

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

11. 6.Hockey stick pattern

12. 7.Fibonacci series

13. 8.Square pattern

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

15. This was all about Pascals’s triangle
Thank-You