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

You are not logged in.

## #51 2013-05-31 03:27:52

bobbym

Online

### Re: triangle inequality

Then 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 2013-05-31 03:29:46

anonimnystefy
Real Member

Online

### Re: triangle inequality

Well, the 83 comes directly from the upper bound.

#### anonimnystefy wrote:

And, what exactly are we doing now. We have the value, we have constructed the triangle. What else is there to do?

Last edited by anonimnystefy (2013-05-31 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 2013-05-31 03:32:40

bobbym

Online

### Re: triangle inequality

The 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 2013-05-31 03:34:03

anonimnystefy
Real Member

Online

### Re: triangle inequality

Well, 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 2013-05-31 03:44:59

bobbym

Online

### Re: triangle inequality

It 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 2013-05-31 03:45:41

anonimnystefy
Real Member

Online

### Re: triangle inequality

There 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 2013-05-31 03:48:19

bobbym

Online

### Re: triangle inequality

With 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 2013-05-31 04:32:01

anonimnystefy
Real Member

Online

### Re: triangle inequality

Well, 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>1/12-1/14=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 2013-05-31 04:38:33

bobbym

Online

### Re: triangle inequality

1/hc>1/12-1/14

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 2013-05-31 04:40:26

anonimnystefy
Real Member

Online

### Re: triangle inequality

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 2013-05-31 04:41:33

bobbym

Online

### Re: triangle inequality

Why 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 2013-05-31 04:44:31

anonimnystefy
Real Member

Online

### Re: triangle inequality

The 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 2013-05-31 04:46:32

bobbym

Online

### Re: triangle inequality

What 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 2013-05-31 04:47:46

anonimnystefy
Real Member

Online

### Re: triangle inequality

Yes, 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 2013-05-31 04:54:38

bobbym

Online

### Re: triangle inequality

I 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 2013-05-31 04:58:27

anonimnystefy
Real Member

Online

### Re: triangle inequality

Well, 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 (2013-05-31 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 2013-05-31 05:02:38

bobbym

Online

### Re: triangle inequality

Hi;

Okay, see you later.

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 2013-05-31 05:17:45

anonimnystefy
Real Member

Online

### Re: triangle inequality

Okay, 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

## #69 2013-06-01 22:19:55

ElainaVW
Full Member

Offline

### Re: triangle inequality

I have a different solution.

Last edited by ElainaVW (2013-06-01 22:28:27)

## #70 2013-06-01 22:20:44

bobbym

Online

### Re: triangle inequality

Hi;

What is it, please post what you have.

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 2013-06-01 22:23:32

ElainaVW
Full Member

Offline

### Re: triangle inequality

#### 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 2013-06-01 22:27:38

bobbym

Online

### Re: triangle inequality

Hi;

That is very good. Nice work.

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.