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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

hi guys

first of all i would like to notice that many threads i started have one word and three exclamation signs.

second,i was just thinking about the many interesting iterations in mathematics and their use.

i know a few iterations,such as Newton's for finding roots of numbers,or the 196 iterarion used for finding if a number is a Lychrel number(none were proven to be such),and many more...

this has come to my mind when i was trying to do something like this:

let us have two actions represented by symbols a and b.

now if we take one of them,say a,than the other one,b,and then take both but in reverse order we get:

abba(which is also a group from sweden (i think!))

now we write that on a piece of paper.next we inverse it all(by substituting a for b and b for a) to get baab.we write that as well.now we write down both but in reverse order to get:

abba baab baab abba

now we repeat like in last two steps to get:

abba baab baab abba baab abba abba baab baab abba abba baab abba baab baab abba

you can continue to do this as long as you want,but when you are finished you can take a piano,or smth like that and take two notes for a and b.it sounds very boring but,hay,at least you know now how to spend 5 minutes of your time on nothing.

btw some geometric iterations are used to get the sierpinski's triangle or the apollonian gasket.

if you know **anything** about **any** iteration/iterations post it here.

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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: 88,589

Hi;

My favorite iteration is:

**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: 15,600

what does it do?

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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: 88,589

Hi;

Did you try it?

**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: 15,600

i don't know how.what is [1,1]?

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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: 88,589

That is a vector consisting of 2 elements.

**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: 15,600

so how do you do this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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First, do you know what the box is?

**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: 15,600

i do not see a box.what box?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,589

Do you know what that box stands for and what it does?

**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: 15,600

is it a matrix?i don't know what it does next to a vector.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,589

See the dot between them? That means multiply them.

**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: 15,600

xaxaxa...:)

i am not that stupid.just i don't know how to multiply a vector and a matrix.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Then I think you should learn and right now! But before you do let us look at the sequence that the above iteration ( and it is an iteration, just disguised as an equation ).

1,1,2,3,5,8,13,...

Recognize those?

**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,never seen them.

just kiding.those are the Fibonacci nums.

where can i have a look at it?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Are you serious? MathsIsFun of course!

**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: 15,600

but where is the vector-matrix product?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,589

near the bottom.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

is that the beef,chicken,vegetable example.

in that case i get [1,2] for k=1

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**bobbym****Administrator**- From: Bumpkinland
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That is correct! Now, how about some matrix by matrix multiplication!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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for k=2 i get (2,3)

for k=3 i get (3,5)

i get it now.

*Last edited by anonimnystefy (2011-09-08 00:36:19)*

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**bobbym****Administrator**- From: Bumpkinland
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First number of each is fibonacci(k+1). That equation solves this recurrence formula.

**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: 15,600

do you know other iterations?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I am working on one right now!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,600

which one?

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