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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

Well, I do not see 30 squares. These √ 3 squares are beyond my visual acuity. I am writing a little program to do this for me.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

ok.but i still want to know what the conclusion is.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

Where r is the number of rows and c is the number of columns. r ≤ c

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

hi bobbym

this can be simplified to:

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

I will tell you why you should never do that lightly.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

why?and do what?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

Simplifcation, which is drummed into school kids is sometimes an error!

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

hi bobbym

i'm not simplifying it because i want to,i'm simplifying it so that i don't have to implement an algorithm for doing combinations.i'm thinking of converting this to the notation you mentioned before in the big Oh thread.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

Even there it might be more useful to think of it in the supposed long form. You could use Stirling's formula on those binomials and go a little further than before perhaps.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

hi bobbym

i'm not sure what you want me to do.could you show me?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

The first one is what is considered mandatory, simplify everything! But it hides the structure of the problem. It is hard to see what combinatorics is involved. The second shows a pattern and might even suggest a starting point for more dimensions or different shapes.

There is a really funny example from an Adrian Oldknow book that demonstrates that stereotyped thinking in math can lead to disaster.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

hi bobbym

i understand what you mean,but,as i stated clearly,i simplified your formula for computational purposes only.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

I know but you must be careful there too

remember?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

how is that possible?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

We did not get into it because you were not ready. The computation you speak of is a very tricky beast. Often in Numerical analysis you anti-simplify because it is superior.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

hi bobbym

this is just basic programming so that's not necessary.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I know, that is what they say. I just mention it so you will be prepared when that comes up.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

ok,thanks!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,904

Ever heard of Adrian Oldknow or his book?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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nope.who's that guy?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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A guy who wrote a nice book on using microcomputers and doing mathematics.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

k,what about him?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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It was just a nice book to read. It showed me that there were alternate ways to do math problems.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

what alternative ways?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Too much to detail, maxima and minima for one.

**In mathematics, you don't understand things. You just get used to them.**

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