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Subject: "Just a Curious Monkey Question...?"     Previous Topic | Next Topic
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Conferences The CTK Exchange Middle school Topic #35
Reading Topic #35
MathWiz
Charter Member
3 posts
Jan-30-01, 04:35 PM (EST)
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"Just a Curious Monkey Question...?"
 
   Why is the pythagorean Therom only true for right triangles?


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  Subject     Author     Message Date     ID  
  RE: Just a Curious Monkey Question.... alexb Jan-30-01 1
     RE: Just a Curious Monkey Question.... MathWiz Feb-06-01 2
         RE: Just a Curious Monkey Question.... alexb Feb-06-01 3
             RE: Just a Curious Monkey Question.... MathWiz (Guest) Feb-07-01 4
                 RE: Just a Curious Monkey Question.... alexb Feb-07-01 5
                     RE: Just a Curious Monkey Question.... MathWiz Feb-07-01 6
                         RE: Just a Curious Monkey Question.... alexb Feb-07-01 7

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alexb
Charter Member
672 posts
Jan-30-01, 04:42 PM (EST)
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1. "RE: Just a Curious Monkey Question...?"
In response to message #0
 
   Assume a, b, c are the sides of a triangle which is not right, but for which nonetheless a2 + b2 = c2.

Position the sides a and b as to make a right angle. Let d be the distance between their endpoints. By the Pythagorean theorem,
a2 + b2 = d2. Which implies

c2 = d2.

From where, c = ±d. However, both c and d are positive from the context. Therefore, c = d in the first place. Therefore, the original triangle was in fact right.


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MathWiz
Charter Member
3 posts
Feb-06-01, 04:42 PM (EST)
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2. "RE: Just a Curious Monkey Question...?"
In response to message #1
 
   What's the connection with the Pythagorean Therom area of squares and Pythagorean Triples?


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alexb
Charter Member
672 posts
Feb-06-01, 04:44 PM (EST)
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3. "RE: Just a Curious Monkey Question...?"
In response to message #2
 
   > What's the connection with the
> Pythagorean Therom area of squares
> and Pythagorean Triples?

I do not understand your question.


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MathWiz (Guest)
guest
Feb-07-01, 09:22 AM (EST)
 
4. "RE: Just a Curious Monkey Question...?"
In response to message #3
 
   I want to know how they are all interalted, if it's not too much to ask. What I want to know is how the area of squares applies tothe Pythagorean Therom, and Pythagorean Triples. How they all fit together.


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alexb
Charter Member
672 posts
Feb-07-01, 11:32 AM (EST)
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5. "RE: Just a Curious Monkey Question...?"
In response to message #4
 
   The Pythagorean theorem asserts that the sum of areas of the squares constructed on the legs of a right triangle equals the area of the square built on its hypotenuse.

Between us, I am uncomfortable answering your questions. This is because I get a feeling that my effort - however small - of typing the answers goes nowhere. You have never followed up on your first question, although I did expect you to.


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MathWiz
Charter Member
3 posts
Feb-07-01, 04:43 PM (EST)
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6. "RE: Just a Curious Monkey Question...?"
In response to message #5
 
   Well, I think that your input that you could give me on to this question would be much greater then any ideas that I could ever come up with, becase your page on proofs for the Pythagorean Therom is truely amazing. Yes, I still am wondering why the Pythagorean Therom is only true for right triangles, becauase I did not understand the frst sentece of your origional response to that question. Any input tht you have would be greatly appreciated. Thank you


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alexb
Charter Member
672 posts
Feb-07-01, 04:51 PM (EST)
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7. "RE: Just a Curious Monkey Question...?"
In response to message #6
 
   >Well, I think that your input
>that you could give me
>on to this question would
>be much greater then any
>ideas that I could
>ever come up with,

Not so, as the last sentence in your message shows very clearly. I can waste plenty of time unless you make some effort at trying to understand both your question and my answer.

> becase
>your page on proofs for
>the Pythagorean Therom is truely
>amazing.

Thank you. But this is irrelevant as you apparently did not get the point.

> Yes, I still
>am wondering why the Pythagorean
>Therom is only true for
>right triangles, becauase I did
>not understand the frst sentece
>of your origional response to
>that question.

The first sentence reads:

Assume a, b, c are the sides of a triangle which is not right, but for which nonetheless a2 + b2 = c2.

Which means, "Assume there is a triangle which is not right but for which the Pythagorean theorem holds nonetheless."

What follows afterwards is a demonstration that that assumption leads to a contradiction.

>Any input
>tht you have would be
>greatly appreciated. Thank you
>



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