Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2011-09-08 21:37:04

anonimnystefy
Real Member

Offline

### Iterations!!!

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.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #2 2011-09-08 21:50:59

bobbym

Online

### Re: Iterations!!!

Hi;

My favorite iteration is:

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #3 2011-09-08 22:03:37

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

what does it do?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #4 2011-09-08 22:04:11

bobbym

Online

### Re: Iterations!!!

Hi;

Did you try it?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #5 2011-09-08 22:04:50

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #6 2011-09-08 22:05:30

bobbym

Online

### Re: Iterations!!!

That is a vector consisting of 2 elements.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #7 2011-09-08 22:05:54

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

so how do you do this?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #8 2011-09-08 22:08:02

bobbym

Online

### Re: Iterations!!!

First, do you know what the box is?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #9 2011-09-08 22:08:48

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

i do not see a box.what box?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #10 2011-09-08 22:10:21

bobbym

Online

### Re: Iterations!!!

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #11 2011-09-08 22:11:13

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #12 2011-09-08 22:12:09

bobbym

Online

### Re: Iterations!!!

See the dot between them? That means multiply them.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #13 2011-09-08 22:13:41

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

xaxaxa...

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #14 2011-09-08 22:16:03

bobbym

Online

### Re: Iterations!!!

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #15 2011-09-08 22:20:18

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

nope,never seen them.

just kiding.those are the Fibonacci nums.

where can i have a look at it?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #16 2011-09-08 22:23:22

bobbym

Online

### Re: Iterations!!!

Are you serious? MathsIsFun of course!

http://www.mathsisfun.com/algebra/matri … lying.html

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #17 2011-09-08 22:25:06

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

but where is the vector-matrix product?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #18 2011-09-08 22:27:11

bobbym

Online

### Re: Iterations!!!

near the bottom.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #19 2011-09-08 22:31:02

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

is that the beef,chicken,vegetable example.

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

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #20 2011-09-08 22:34:13

bobbym

Online

### Re: Iterations!!!

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

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #21 2011-09-08 22:35:39

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

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 22:36:19)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #22 2011-09-08 22:39:26

bobbym

Online

### Re: Iterations!!!

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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #23 2011-09-08 22:40:43

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

do you know other iterations?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

## #24 2011-09-08 22:41:16

bobbym

Online

### Re: Iterations!!!

I am working on one right now!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

## #25 2011-09-08 22:43:51

anonimnystefy
Real Member

Offline

### Re: Iterations!!!

which one?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón