Pascal Triangle & Its Applications.

[mubashirmansoor]

Hello,

I have searched through out the internet but I couldn't find any information about the origin of Pascal Triangle & how it came into being... Because I am sure that such a precise & accurate numerical array didn't come out of no where !

I will be very thankful for your guidance.

My second question is about the applications of this array, except Binomial expansion.

Many thanks for giving me the time.

 

[huba]

I think there is a lot of information about this topic on the internet.
As so often, a useful starting point is Wikipedia (see "Pascal's triangle").
You can also search Amazon.com; for instance, a review on 'Pascal's Arithmetical Triangle: The Story of a Mathematical Idea' (Edwards, A.W.F, 2002) describes the book as "an impressive culmination of meticulous research into original sources, this definitive study constitutes the first full-length history of the Arithmetic Triangle."

 

[mubashirmansoor]

Many thanks for introducing the book, huba.

I will try to find it from somewhere :)

Any further comments will be highly appreciated.

 

[mathwonk]

once you know the binomial coefficients satisfy (n,k) = "n choose k"

= (n-1,k) + (n-1,k-1), what else is there to say about pascal's triangle?

i.e. each entry is obtained from adding the two previous ones.

 

[mubashirmansoor]

What I would like to know is what made Pascal, Omar Khayam or the Chinese mathematicians to build such an array which is obtained from adding the previous ones...

Because it simply contains dozens of very interesting patterns!

 

[HallsofIvy]

The obvious thing is that they got it from the binomial expansion.

 

[hadi amiri 4]

did you know a iranian mathmatican (khayam)had found this before pascal

 

[roam]

did you know a iranian mathmatican (khayam)had found this before pascal

Yep, I knew that. He didn't find it but he studied it many centuries prior to Pascal. Actually it's supposed to be called "Khayyam-Pascal triangle"!

Mind you, some western authors have tried to revise the history...