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You are not logged in. #51 20130531 03:27:52
Re: triangle inequalityThen I used a couple of more relationships and the triangle inequality to test the integers from 7 to 84. 83 was the biggest. 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. #52 20130531 03:29:46
Re: triangle inequalityWell, the 83 comes directly from the upper bound.
Last edited by anonimnystefy (20130531 03:32:37) 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #53 20130531 03:32:40
Re: triangle inequalityThe upper bound I showed is 84. 83 works but 84 does not. 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. #54 20130531 03:34:03
Re: triangle inequalityWell, of course it doesn't work. The triangle inequality states a+b>c, not >=c. 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #55 20130531 03:44:59
Re: triangle inequalityIt took a little M code to try from 7 to 84. 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. #56 20130531 03:45:41
Re: triangle inequalityThere was no need to try them, but whatever. 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #57 20130531 03:48:19
Re: triangle inequalityWith what I dug up, I had to try them all. What did you have to shorten that? 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. #58 20130531 04:32:01
Re: triangle inequalityWell, I had the fact that the lengths 1/12, 1/14 and 1/hc must form a triangle, where 1/hc is as small as possible. Because of the triangle inequality we have that 1/hc>1/121/14=1/84. So, hc<84. The maximum possible length is 83. 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #59 20130531 04:38:33
Re: triangle inequalityOkay but what about this? 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. #60 20130531 04:40:26
Re: triangle inequalityWhat about 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #61 20130531 04:41:33
Re: triangle inequalityWhy the minus and not a plus? 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. #62 20130531 04:44:31
Re: triangle inequalityThe triangle inequality states that 1/hc+1/14>1/12. 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #63 20130531 04:46:32
Re: triangle inequalityWhat triangle? That inequality is for the sides. You have altitudes there. 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. #64 20130531 04:47:46
Re: triangle inequalityYes, but, as I already said, 1/ha=1/12, 1/hb=1/14 and 1/hc must be length of some triangle in order to be a valid set of altitudes. 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #65 20130531 04:54:38
Re: triangle inequalityI do not get it but it works so the problem is done. 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. #66 20130531 04:58:27
Re: triangle inequalityWell, it is because a*ha=b*hb=c*hc. From this we can get a:b:c=(1/ha):(1/hb):(1/hc), which means that, if a, b and c can form a triangle, 1/ha, 1/hb and 1/hc must be able to form a triangle as well. Last edited by anonimnystefy (20130531 04:58:35) 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #67 20130531 05:02:38
Re: triangle inequalityHi; 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. #68 20130531 05:17:45
Re: triangle inequalityOkay, see you! 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 “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #70 20130601 22:20:44
Re: triangle inequalityHi; 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. #71 20130601 22:23:32
Re: triangle inequality[Code fixed by admin] Code:Solve[{12 ==1/a Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c)  a) (1/2 (a + b + c)  b) (1/2 (a + b + c)  c)), 14 == 1/b Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c)  a) (1/2 (a + b + c)  b) (1/2 (a + b + c)  c)), 83 == 1/c Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c)  a) (1/2 (a + b + c)  b) (1/2 (a + b + c)  c)), 12 == (b*c)/(2 R)}, {a, b, c, R}] // N Only had to try 84 and 83. #72 20130601 22:27:38
Re: triangle inequalityHi; 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. 