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## #1 2006-02-15 10:49:43

MathsIsFun
Registered: 2005-01-21
Posts: 7,631

### Pascal's Triangle

Just done another page: Pascal's Triangle (and what an interesting thing it is!), any suggestions?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #2 2006-02-15 10:55:58

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Pascal's Triangle

Anyway, it seems very good. I can't see any mistakes and you've covered it fairly comprehensively. All I can suggest is maybe some pictures of patterns you can get for different multiples (or if you're feeling adventurous, maybe even some kind of program that will show the multiple patterns of a number that we can specify), and also to include the fibonacci pattern that you can get from knight's move, because that's just uber-cool.

Edit: That page links to the Tetrahedral Numbers page and there's a mistake there. The illustration shows a tetrahedron of height 5.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2006-02-15 11:34:36

MathsIsFun
Registered: 2005-01-21
Posts: 7,631

### Re: Pascal's Triangle

Thanks, fixing it now.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #4 2006-02-15 17:56:14

justlookingforthemoment
Moderator
Registered: 2005-05-26
Posts: 2,161

### Re: Pascal's Triangle

Like always, brilliant work.

Pascal's triangle is so cool! There are so many interesting things you can find hidden in it!

You covered quite a lot but there's far too many to list...
 Probability - rows represent the number of ways coins can be tossed up.
 Each row is 11^n, n being the row number
 In the 'triangular numbers' row you have highlighted, if you add two numbers next to each other you get the sequence of square numbers.
 If you separate the numbers into rows (like in the picture below) and add the numbers in each row... you get the Fibonacci sequence.

Oh, and mathsy - you beat me to it!

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## #5 2006-02-15 19:21:09

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Pascal's Triangle

But you didn't explain what it's good for...polynomial expansion!

El que pega primero pega dos veces.

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## #6 2006-02-16 00:57:36

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,812

### Re: Pascal's Triangle

Great!
ryos is right, nowhere in the page has it been mentioned that the numbers in the Pascal's triangle are coefficients of the first, second, third,......terms in the binomial expansion. Illustrations of (a+b)², (a+b)³, (a+b)^4, (a+b)^5 etc. may also be given in the page. The numbers in the rows of Pascal's triangle can be compared to nC0, nC1, nC2, nC3,....nCr etc. (like 3C0, 3C1, 3C2, 3C3 for (a+b)³) to explain their being equivalent.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #7 2006-02-16 01:54:04

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

### Re: Pascal's Triangle

I think its great.There are so many number patterns there.:)

Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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## #8 2006-02-16 04:17:00

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Pascal's Triangle

Lots of great ideas there. Just one thing:

justlookingforthemoment wrote:

 Each row is 11^n, n being the row number.

Only for the first few rows. The pattern is ruined when you get rows that contain numbers more than 9.

Why did the vector cross the road?
It wanted to be normal.

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## #9 2006-02-16 08:34:17

MathsIsFun
Registered: 2005-01-21
Posts: 7,631

### Re: Pascal's Triangle

Thanks guys! I will get on to it.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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