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#26 2012-09-30 08:16:47
- bobbym
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Re: Triangle Problem
Supposing a was large and b,c were small? I do not know if that step is rigorous enough or requires more.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#27 2012-09-30 08:45:40
- anonimnystefy
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Re: Triangle Problem
You are forgeting one thing which might be crucial. a, b and c are sides of a triangle. There is a great chance that has some other purpose than just stating that a, b and c are positive.
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
#28 2012-09-30 08:56:54
- bobbym
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Re: Triangle Problem
One property is
a + b > c
a + c > b
b + c > a
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#29 2012-09-30 09:00:59
- anonimnystefy
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Re: Triangle Problem
Exactly what I had in mind. I will try to do the problem.
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
#31 2012-09-30 19:49:38
- zetafunc.
- Guest
Re: Triangle Problem
bob bundy wrote:
hi
But a, b, c all > 0
Similarly
Bob
Thanks for this, I didn't think about setting c(b+a) > 0... so, would all my reasoning be mathematically sound? I agree with what you have written above -- I'm wondering if a geometric solution is also possible however, since it appears that this solution doesn't take advantage of any triangle properties...
#32 2012-09-30 19:59:27
- bob bundy
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Re: Triangle Problem
hi zetafunc
Your post with (a+1)(b+1)(c+1) = 4 + (a-1)(b-1)(c-1) is the way to go with this.
But you just needed to justify a,b,c all < 1
I experimented using Sketchpad with a number of values for a b and c and found
it doesn't hold if a b c are not the sides of a triangle and the expression = 4 when any of a b or c = 1. (and is > 4 if over 1)
So the two constraints (triangle and ab + bc + ca = 1) are necessary.
Therefore you have to use a property of triangles.
My contribution uses b < a + c
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#33 2012-09-30 20:05:10
- anonimnystefy
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Re: Triangle Problem
bob bundy wrote:
How'd you get 2b<b(a+c)? It would imply that a+c>2, so one of them has to be greater than 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
#34 2012-09-30 20:24:08
- bob bundy
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Re: Triangle Problem
Arhh! Once more you have spotted my error. Curses. (not aimed at you of course!)
My brain did this.
triangle property
b < a + c and b(a+c) < 2 .... => 2b < 2.
But it was wishful thinking.
I should have written b^2 < 2 which is not any help. Sorry zetafunc. Back to the drawing board.
Bob
ps. Nevertheless, some triangle property seems essential here.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#35 2012-09-30 20:48:56
- anonimnystefy
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Re: Triangle Problem
It's okay. For I second there I thought we finally had proof!
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
#36 2012-10-01 04:27:20
- bobbym
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Re: Triangle Problem
Hi zetafunc.;
zetafunc wrote:
a(b + c) + bc = 1
b(a + c) + ca = 1
c(a + b) + ab = 1
You were on the right track when you posted that.
You need to prove that a,b,c <1.
Let's assume WLOG that a>1 then
By the triangle inequality
If a>1 then (b+c) > 1 and a(b+c) >1 but bc cannot be less than or equal to 0 ( see equation 2 ) so we have a contradiction. Therefore a,b,c<1
Now put your proof all together and present it.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#37 2012-10-02 01:29:59
- zetafunc.
- Guest
Re: Triangle Problem
I see now. Thank you.
I suppose the proof would look like this:
#38 2012-10-02 04:06:20
- bobbym
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Re: Triangle Problem
Hi;
Yes, that is what I would do. If it is wrong then at least you have company.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.