1,1,2,3,5,8,13,21...
Author  protectedlord 

Tags  author:protectedlord cooltastic curves golden nart rated ratio 
Created  20090408 
Last Modified  20090408 
Rating 
4 by 25 people.

Map Data  
Description  Kudos if you recognize it. Mathematically, this is a beautiful map. my first Nart... (getting the curve and proportions right was a challenge(check it your self)  this took a lot longer then it looks.) 
Other maps by this author
Comments
20090415
Hahaha
I'm surprised this map got an average of 3: The ignorant rated it 0 and the informed ignored the rating and just started exchanging mathematical proofs.
20090413
Actually, It just really
depends on your way of rounding.
Yeah, I guess that is the easiest proof.
Sum(k=1..inf){10^k} = 1/9, therefore 9*Sum(k=1..inf){10^k} = 1
Another onestep proof for .99999 = 1 is...
By the Geometric Series Theorum, since 1/10 < 1
9*Sum(k=0..inf){10^k} = 9/(1(1/10)) = 9/(9/10) = 1/(1/10) = 10
.: 9.9999... = 10
.: 0.9999... = 1
Sum(k=1..inf){10^k} = 1/9, therefore 9*Sum(k=1..inf){10^k} = 1
Another onestep proof for .99999 = 1 is...
By the Geometric Series Theorum, since 1/10 < 1
9*Sum(k=0..inf){10^k} = 9/(1(1/10)) = 9/(9/10) = 1/(1/10) = 10
.: 9.9999... = 10
.: 0.9999... = 1
20090410
MATHS IS NOT BROKEN!
@_Null
"If .3333... (or 1/3) + .6666... (or 2/3), then shouldn't .9999... = 1?
Or this (Try to follow these steps):
Given A=B
1. Multiply both sides by A: A*A=A*B
2. Subtract B^2 from both sides: A^2  B^2=A*BB^2
3. Factor: (A+B)*(AB)=B(AB)
4. Simplify: A+B=B
5. Substitute A for B: B+B=B
6. 2B=B
7. Divide both sides by B: 2=1
I BROKE MATH!!!! AAHHHH!!!!"
STEP 4 CANNOT BE DONE BECAUSE YOU COULD BE DIVIDING BY 0.
I saw this on a poster at school.
"If .3333... (or 1/3) + .6666... (or 2/3), then shouldn't .9999... = 1?
Or this (Try to follow these steps):
Given A=B
1. Multiply both sides by A: A*A=A*B
2. Subtract B^2 from both sides: A^2  B^2=A*BB^2
3. Factor: (A+B)*(AB)=B(AB)
4. Simplify: A+B=B
5. Substitute A for B: B+B=B
6. 2B=B
7. Divide both sides by B: 2=1
I BROKE MATH!!!! AAHHHH!!!!"
STEP 4 CANNOT BE DONE BECAUSE YOU COULD BE DIVIDING BY 0.
I saw this on a poster at school.
20090410
The golden ratio!!
Cool. You should've used gold for the curve though.
20090409
@ exuberance
Yeah, well there are also 10 kinds of people in this world: those that understand binary and those that don’t. lol my cheese comment got deleted :(
20090408
Skippy
your ignorant, why don't you look up what the golden spiral represents. It means more than your little mind can fathom I suppose.
20090408
Again...
wt*... is this about? a spiral of mines man, all u, why are u still posting...
All this is bla bla blah over a ****en spiral of mines.
Mines and like wat, 45 comments? the thing
doesnt
represent
any
thing
U all are making a big fuss over something that wont even change anything.
U sound like nerds (why? because i got no idea what this map is for and what u guys are saying...)
All this is bla bla blah over a ****en spiral of mines.
Mines and like wat, 45 comments? the thing
doesnt
represent
any
thing
U all are making a big fuss over something that wont even change anything.
U sound like nerds (why? because i got no idea what this map is for and what u guys are saying...)
20090408
If your comment was for
me exuberance that was clearly a presumption in my argument but as you said a reacurring decimal is obviously convergent nobody would dissagree so I though it reasonable whereas many people do try to argue the case for 1 as seperate from 0.999... and therefor its isn't obvious to everyone see the topic in the forums for example.
Yes, the proof in the last post is incorrect. It does have the right conclusion, but when you say .99999... what you mean is SUM(n=1..inf). And although it is very obvious looking at it that this converges to a number (it should also be obvious that it converges to 1), you still need to actually prove that. Obviously it's not going to diverge to infinity, but you still need to prove it until you can subtract the 2 sums since you cannot subtract divergent series.
It is easy to prove that this series converges, however. Consider the 0.99999... series. (the 9.9999... is just 10 times that). The n+1st term is 9*10^(n1) and the nth term is 9*10^n. Now, use the ratio test to find lim((n1)/n) = lim((9*10^(n1))/(9*10^n)) = lim(10^1) = lim(0.1) = 0.1. And since 0.1 < 1, therefore the series converges absolutely. You can now subtract the series and continue with your proof.
Therefore SUM(9*10^n) = 1.
It is easy to prove that this series converges, however. Consider the 0.99999... series. (the 9.9999... is just 10 times that). The n+1st term is 9*10^(n1) and the nth term is 9*10^n. Now, use the ratio test to find lim((n1)/n) = lim((9*10^(n1))/(9*10^n)) = lim(10^1) = lim(0.1) = 0.1. And since 0.1 < 1, therefore the series converges absolutely. You can now subtract the series and continue with your proof.
Therefore SUM(9*10^n) = 1.
20090408
So is it
the golden ratio spiral or the fibonacci spiral the difference is important.
you might find this map interesting http://nmaps.net/151888
As for _Null your logic is flawed
to get from steps 3 and 4 you devide by (AB)
however if A=B then AB=0
any argument which contains devision by 0 is nonsence and will lead to contradictions that isn't anyting new and you haven't broken maths you've just broken the rules of maths. If you break the rules of maths you can "prove" anything = anything you want.
Your first argument is better I think there is a topic on it in the forums I like this version of it
a=0.999...
10a=9.999...
9a=10aa
=9.999...0.999...
=9
a=1
you might find this map interesting http://nmaps.net/151888
As for _Null your logic is flawed
to get from steps 3 and 4 you devide by (AB)
however if A=B then AB=0
any argument which contains devision by 0 is nonsence and will lead to contradictions that isn't anyting new and you haven't broken maths you've just broken the rules of maths. If you break the rules of maths you can "prove" anything = anything you want.
Your first argument is better I think there is a topic on it in the forums I like this version of it
a=0.999...
10a=9.999...
9a=10aa
=9.999...0.999...
=9
a=1
20090408
Well...
If .3333... (or 1/3) + .6666... (or 2/3), then shouldn't .9999... = 1?
Or this (Try to follow these steps):
Given A=B
1. Multiply both sides by A: A*A=A*B
2. Subtract B^2 from both sides: A^2  B^2=A*BB^2
3. Factor: (A+B)*(AB)=B(AB)
4. Simplify: A+B=B
5. Substitute A for B: B+B=B
6. 2B=B
7. Divide both sides by B: 2=1
I BROKE MATH!!!! AAHHHH!!!!
As for the spiral, it looks great. 4/5
Or this (Try to follow these steps):
Given A=B
1. Multiply both sides by A: A*A=A*B
2. Subtract B^2 from both sides: A^2  B^2=A*BB^2
3. Factor: (A+B)*(AB)=B(AB)
4. Simplify: A+B=B
5. Substitute A for B: B+B=B
6. 2B=B
7. Divide both sides by B: 2=1
I BROKE MATH!!!! AAHHHH!!!!
As for the spiral, it looks great. 4/5
20090408
Oye!!
The map may not be spectacular, but you truly have to be intellectual to appreciate the fibonacci. So to all you haters, I pity the fool.
20090408
Wow, cause this really matters
What a waste of time, it's depressing that people would rate and comment on this compared to some of the other maps. I'm not sniping I'm just giving it a 0.
20090408
ha, nice breakdown taco ;]
20090408
ha this is simple
trying to find an equation on a three dementional graph and knowing the types of equations out there to figure it out, o and logarythims and inverses are also in the bunch of equation finding
X°
X°
20090408
nobody's going to check your work
i think its stupid how something like this got so many rates.
still, kudos to you if you did go thru the trouble, i just dont think it would be worth it.
still, kudos to you if you did go thru the trouble, i just dont think it would be worth it.
20090408
Nerds UNITE!!!
Surprisingly my picture is an umlauted 'o'. Coincidence exuberance? I think not!!!
20090408
...
WHAT THE **** IS SO COOL ABOUT A SPIRAL?
Seriously 30 comments over a spiral of mines, what does it represent anyway?
To hell, 30 comments. I don't see anything. NR...
Seriously 30 comments over a spiral of mines, what does it represent anyway?
To hell, 30 comments. I don't see anything. NR...
When rounding to the nearest number for a number k+.5 for k an integer, there's 2 main ideas:
1) always round up
2) round to the even number
I propose a new strategy!
Do not round 2.5 to 2 or to 3. round it to both 2 AND 3! 2.5 = 2+ö where ö is simultaneously 0 AND 1. I dub this contradiction of a number Schrödinger's number! HOORAY!
Yes, I just created quantum numbers! That's even worse than imaginary numbers since they make no sense!
1) always round up
2) round to the even number
I propose a new strategy!
Do not round 2.5 to 2 or to 3. round it to both 2 AND 3! 2.5 = 2+ö where ö is simultaneously 0 AND 1. I dub this contradiction of a number Schrödinger's number! HOORAY!
Yes, I just created quantum numbers! That's even worse than imaginary numbers since they make no sense!
20090408
My Statement still stands
He says almost perfect so 4.499999, would round up to 4.5.
Now 4.59 would round up to 5.
Now 4.59 would round up to 5.
20090408
fibonnacioh
yay!
20090408
Hmm...
On the subject of rounding I though that it was in practise to round up at 5s but in reality to be fair we should round up some of the time and down other times. This is because for example numbers ranging from 1 to 2.
10o does not round... nor does 2.0. They are already solid.
.1, .2, .3, .4 all round down. So 4 numbers round down. But 5 round up:
.5, .6, .7, .8 and .9. So really you should round up half the time and down the other half with 5s so that it becomes 4.5 numbers round up and 4.5 numbers round down... I think
10o does not round... nor does 2.0. They are already solid.
.1, .2, .3, .4 all round down. So 4 numbers round down. But 5 round up:
.5, .6, .7, .8 and .9. So really you should round up half the time and down the other half with 5s so that it becomes 4.5 numbers round up and 4.5 numbers round down... I think
Nice curve.
DemonzLunchBreak
Oh, nice.