ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Voltman on March 13, 2009, 09:24:57 pm

Title: Pascal's triangle
Post by: Voltman on March 13, 2009, 09:24:57 pm: In year 12 methods, do you need to memorise Pascal's Triangle?
Title: Re: Pascal's triangle
Post by: TrueTears on March 13, 2009, 09:26:50 pm: you should as it is helpful for binomial expansion, to be honest pascals triangle isn't hard to remember anyway :)
Title: Re: Pascal's triangle
Post by: Voltman on March 13, 2009, 09:43:19 pm: Quote from: TrueTears on March 13, 2009, 09:26:50 pm
you should as it is helpful for binomial expansion, to be honest pascals triangle isn't hard to remember anyway :)

To which row?
Title: Re: Pascal's triangle
Post by: mano91 on March 13, 2009, 09:50:59 pm: you would probably need to know up to Power of 5.
never got any further than that.
Title: Re: Pascal's triangle
Post by: Voltman on March 13, 2009, 09:53:44 pm: Hmmm...I'll add a big one as a screensaver just in case (15 rows).
Title: Re: Pascal's triangle
Post by: shinny on March 13, 2009, 09:55:16 pm: I assume you haven't actually noticed the pattern if you're asking this...look at it like this;

   0 1 0
   0 1 1 0
   0 1 2 1 0
   0 1 3 3 1 0
   0 1 4 6 4 1 0

Basically, for any row, the number that should be there is the sum of the two numbers surrounding it in the row above. I've put the 0's there to make this more obvious. e.g. For the 5th row, the first number is 1 as 0+1 is 1, second number is 4 as 1+3 if 4 and so on.

As you can see, it's VERY easy to remember for an indefinite number of rows.

EDIT: Or perhaps you knew this pattern and was just wanting to memorise for time measures? In that case, don't bother. You've got plenty of time to draw this up (you'll never need to go very far down anyway) and drawing it up on the spot according to this pattern is less likely to cause you mistakes than recall errors will.
Title: Re: Pascal's triangle
Post by: kamil9876 on March 13, 2009, 10:51:14 pm: Or you can just use combinatorics:

e.g: $7C4=\frac{7*6*5*4}{1*2*3*4}$

and you have things cancelling very nicely: plus u don't need to calculate all the rows from 1-6 to get row 7. Plus u can use the fact that it's symmetrical to save almost half the calculation time i.e symmetrical because nCk=nC(n-k).
Title: Re: Pascal's triangle
Post by: IntoTheNewWorld on March 13, 2009, 11:06:34 pm: I personally think pascal's triangle is better than combinatorics for this purpose, it really doesn't take that long to do quite a few rows, and it's easier (and less prone to errors) to do binomial expansion using a row from pascal's triangle imo.
Title: Re: Pascal's triangle
Post by: Voltman on March 13, 2009, 11:16:17 pm: Quote from: shinny on March 13, 2009, 09:55:16 pm
EDIT: Or perhaps you knew this pattern and was just wanting to memorise for time measures? In that case, don't bother. You've got plenty of time to draw this up (you'll never need to go very far down anyway) and drawing it up on the spot according to this pattern is less likely to cause you mistakes than recall errors will.

Yes...I was aware of that pattern.
Title: Re: Pascal's triangle
Post by: shinny on March 13, 2009, 11:19:36 pm: Well like I said, there's definitely no need to memorise the rows themselves. Just redraw it every time and that's enough.
Title: Re: Pascal's triangle
Post by: TrueTears on March 13, 2009, 11:21:32 pm: Quote from: shinny on March 13, 2009, 11:19:36 pm
Well like I said, there's definitely no need to memorise the rows themselves. Just redraw it every time and that's enough.
yeap, that's exactly what I do when I do binomial expansion and it's much less prone to error.
Title: Re: Pascal's triangle
Post by: kurrymuncher on March 14, 2009, 12:21:17 am: Dont waste your time
Title: Re: Pascal's triangle
Post by: Damo17 on March 14, 2009, 12:29:48 am: In my opinion, as Shinny said just remember the pattern and you can't go wrong. It would be a waste of time memorising many rows if you know the pattern.