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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

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THE POINCARE CONJECTURE PROOF - By Anthony.R.Brown 12/06/07

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Problem = " How Can you Distinguish an Apple from a Doughnut "

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The Poincare Conjecture Truth Table

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APPLE : DOUGHNUT

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IS IT A FRUIT Yes : No

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IS IT MADE OF DOUGH No : Yes

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DOES IT GROW ON A TREE Yes : No

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IS IT MADE BY HUMANS No : Yes

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The Above Poincare Conjecture Truth Table,shows clearly how to Distinguish an Apple from a Doughnut!

Of course there are other Fruits and Food that will fit the Table,But we know the Problem Only involves an Apple and a Doughnut,as in the Question?

A.R.B

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

I believe you already posted this once, and it was moved to the Jokes forum. You should go look at thread there instead of re-posting it.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys

You dont have to try and tell me what I have Posted! I should know Because I Know what Iv'e Posted!

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Below is the FOOLS! Answer!!...............................................................................................

Poincaré Conjecture

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If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

Anthony.R.Brown wrote:

To Maelwys

You dont have to try and tell me what I have Posted! I should know Because I Know what Iv'e Posted!

All I meant to do was suggest that instead of duplicating posts, you should try to keep discussions to a single thread per discussion. If you believe that your thread is better placed on this board instead of the Jokes board, message one of the moderators, explain your reasoning, and ask him to move it. Simply reposting it against the moderator's move just breaks up discussion about the thread to two separate places, and causes clutter on two separate boards.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

There WAS this one: http://www.mathsisfun.com/forum/viewtopic.php?id=7473 (since edited) and I really thought it was just in fun!

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

What Is the Conjecture?

Poincaré's Conjecture deals with the branch of math called topology, which is the study of shapes, spaces, and surfaces. The Clay Institute offers this deceptively friendly-sounding doughnut-and-apple explication of the bedeviling problem:

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Quote:"

All I meant to do was suggest that instead of duplicating posts, you should try to keep discussions to a single thread per discussion. If you believe that your thread is better placed on this board instead of the Jokes board, message one of the moderators, explain your reasoning, and ask him to move it. Simply reposting it against the moderator's move just breaks up discussion about the thread to two separate places, and causes clutter on two separate boards. "

WHY SHOULD I? THE PROOF STANDS! IT'S AN INSULT TO JUST MOVE SOMETHING TO ANOTHER POST! BY SOMEONE THAT HAS NEVER PROVED ME WRONG IN ANY MATH POST'S OF MINE!

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

Okay, now that the other thread has apparantly been dematerialized, we can move discussion here.

I don't understand the point of your initial argument. Poincaré was discussing different properties of three dimensional shapes, specifically those that do or do not have simple meeting points (a sphere vs a torus) using the examples of an apple and a doughnut. You're simply comparing various other properties of an apple and a doughnut that are unimportant to the property being used in the proof, the basic shape. So how does your proof relate to Poincaré's work?

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys

A.R.B

You need to read Post #4

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

Anthony.R.Brown wrote:

To Maelwys

A.R.B

You need to read Post #4

I did, and I think it's an extremely interesting conjecture. I just don't understand what the dough vs fruit properties of the two items have to do with the unique properties of their shapes (sphere vs torus)

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

No. I don't believe it. I *can't bring myself* to believe it. It's just impossible.

You *seriously* didn't mean for this to be a joke? Oh... My... Science...

And here I thought it was hilarious.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

WHY SHOULD I? THE PROOF STANDS! IT'S AN INSULT TO JUST MOVE SOMETHING TO ANOTHER POST! BY SOMEONE THAT HAS NEVER PROVED ME WRONG IN ANY MATH POST'S OF MINE!

Anthony, I honestly thought you were just making a joke. A rather funny joke in my opinion.

But you misunderstand the problem. They use "apple" and "donut" as analogies, to give those who don't have enough mathematical knowledge a fighting chance to understand the problem. They don't actually mean a donut and apple.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Ricky

Quote:" Anthony, I honestly thought you were just making a joke. A rather funny joke in my opinion.

But you misunderstand the problem. They use "apple" and "donut" as analogies, to give those who don't have enough mathematical knowledge a fighting chance to understand the problem. They don't actually mean a donut and apple. "

A.R.B

The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )

Poincaré Conjecture

--------------------------------------------------------------------------------

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

Anthony.R.Brown wrote:

The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )

Yes, he's using apples, doughnuts, and rubber bands to simplify the problem. But what he's really discussing is the problem that when you bisec a sphere or a torus with a single line across the middle, it's possible to reduce the area of the section sliced by the line to a single point on a sphere, but not on a torus. But just because he uses one simplified method to explain doesn't mean that his example encapsulates every part of the original problem, or that his example can be examined and counterpointed as the only argument he has.

That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples, I'll have 4 apples. And then I could counter that by saying "No, 2 + 2 = 3, because one of those apples probably has a worm in it and then I'll just have to throw it out anyway, so it doesn't really count". You can only take an example to a certain point in math. ;-)

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys

A.R.B

Do you never Notice who the Posts are Addressed to.........................................................

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys

Quote:" That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples, I'll have 4 apples. And then I could counter that by saying "No, 2 + 2 = 3, because one of those apples probably has a worm in it and then I'll just have to throw it out anyway, so it doesn't really count". You can only take an example to a certain point in math. ;-) "

A.R.B

The Apples can have a Million worms! and you can throw away as many Apples as you want! Nothing will change the fact! that from the Start you had 4 Apples!!....................................

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

if you really want to take it that literally, he actually had 2 apples to start with ^.^

The Beginning Of All Things To End.

The End Of All Things To Come.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Quote:" That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples

Have and Gave is the Start of the Problem ( 2 + 2 = 4 )

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )

Again Anthony, that's not the original problem. That is a description of the problem given to people who are not literate in topology. This is the Poincare conjecture:

Every simply connected closed three-manifold is homeomorphic to the three-sphere.

Do you now see why we don't tell people the actual mathematical problem? Almost no one would understand it!

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**ben****Member**- Registered: 2006-07-12
- Posts: 106

But you seem not to understand that what you you call "apples" (2-sphere) and "doughnuts" (2-torus) are classic examples of 2-manifolds. The P. conjecture is relatively easy to prove in the 2-dimensional case, exceptionally difficult for the 3-manifold case. Hence the prize. Ricky has it right; this is the Poincaré conjecture:

Ricky wrote:

Every simply connected closed three-manifold is homeomorphic to the three-sphere.

So, before you start spouting off your nonsense, make sure that (at the very least) you understand what a manifold is, what it means for it to be connected and what the word homeomorphic means. Until you have that under your belt, you are not qualified to comment.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

I Fully Understand the Problem!

But in a Sarcastic way I'm showing How Math Simplified Examples! can make the Situation Worse! by Giving Examples Using Items like Rubber Bands! Apples! Doughnuts!

Far Better from the Start to Give actual Examples! and Simplified Math to explain the Problem!

A.R.B

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Ben

Quote:" But you seem not to understand that what you you call "apples" (2-sphere) and "doughnuts" (2-torus) are classic examples of 2-manifolds.

A.R.B

Some Doughnuts can be the Same Round Shape as an Apple!!

*Last edited by Anthony.R.Brown (2007-06-15 01:20:39)*

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

Anthony.R.Brown wrote:

Some Doughnuts can be the Same Round Shape as an Apple!!

Yes, the entire "proof" clearly falls apart if you take timbits (doughnut holes, or whatever else you call them) into account. Even jelly-filled doughnuts would disrupt this proof! Clearly Poincaré wasn't thinking clearly and his entire work should be thrown out the window for these heinous oversights. ;-)

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys!

At Last we Agree on Something!...........................................................................................

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