Pascal Triangle & Its Applications.

Click For Summary
The discussion centers on the origins and historical context of Pascal's Triangle, highlighting its development by mathematicians like Omar Khayyam and its earlier existence in Chinese mathematics. Participants note that while the triangle is well-known for its connection to binomial expansion, it also contains numerous patterns worthy of exploration. A recommended resource is the book "Pascal's Arithmetical Triangle," which provides a comprehensive history of the concept. The conversation touches on the need for accurate historical attribution, suggesting that Khayyam's contributions predate Pascal's work. Overall, the discussion emphasizes the triangle's mathematical significance and the importance of recognizing its historical roots.
mubashirmansoor
Messages
258
Reaction score
0
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.
 
Physics news on Phys.org
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."
 
Many thanks for introducing the book, huba.

I will try to find it from somewhere :)

Any further comments will be highly appreciated.
 
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.
 
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!
 
The obvious thing is that they got it from the binomial expansion.
 
did you know a iranian mathmatican (khayam)had found this before pascal
 
hadi amiri 4 said:
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...
 

Similar threads

Quadratics using Pascal's triangle
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Primality test from pascal triangle
  • · Replies 3 ·
Replies
3
Views
2K
Proving natural numbers in Pascal's Triangle
  • · Replies 21 ·
Replies
21
Views
6K
Perimeter relationships -- Dividing a rectangle into 4 triangles
  • · Replies 2 ·
Replies
2
Views
3K
Admissions How to improve graduate school applications after college?
  • · Replies 32 ·
2
Replies
32
Views
4K
Pascal's Triangle: Pointers and Dynamic Memory Allocation
  • · Replies 2 ·
Replies
2
Views
3K
Symmetries of a Tetrahedron video
  • · Replies 1 ·
Replies
1
Views
2K
Estimating the velocity of seismic waves through an idealized Earth
  • · Replies 6 ·
Replies
6
Views
2K
Admissions PhD Admission: What Do Committees Want from an MS Applicant in Research?
  • · Replies 5 ·
Replies
5
Views
659
Pascal's Triangle and Binomial Theorem
  • · Replies 4 ·
Replies
4
Views
5K