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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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: 82,753

Hi;

My favorite iteration is:

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

what does it do?

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: 82,753

Hi;

Did you try it?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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

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: 82,753

That is a vector consisting of 2 elements.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

so how do you do this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

First, do you know what the box is?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

i do not see a box.what box?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

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

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

See the dot between them? That means multiply them.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

xaxaxa...:)

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

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?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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
- Posts: 82,753

Are you serious? MathsIsFun of course!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

but where is the vector-matrix product?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

near the bottom.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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
- Registered: 2009-04-12
- Posts: 82,753

That is correct! Now, how about some matrix by matrix multiplication!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

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)*

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

First number of each is fibonacci(k+1). That equation solves this recurrence formula.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

do you know other iterations?

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 82,753

I am working on one right now!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,860

which one?

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

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