I found the following at http://www.scribd.com/doc/30552/A-Calculus-Proof-of-the-Pythagorean-Theorem

I do not know the author, but it seems to me a strong counterexample to the Pythagorean Proposition:

<a title="View A Calculus Proof of the Pythagorean Theorem on Scribd" href="http://www.scribd.com/doc/30552/A-Calculus-Proof-of-the-Pythagorean-Theorem"; style="margin: 12px auto 6px auto; font-family: Helvetica,Arial,Sans-serif; font-style: normal; font-variant: normal; font-weight: normal; font-size: 14px; line-height: normal; font-size-adjust: none; font-stretch: normal; -x-system-font: none; display: block; text-decoration: underline;">A Calculus Proof of the Pythagorean Theorem</a> <object id="doc_419953862916615" name="doc_419953862916615" height="600" width="100%" type="application/x-shockwave-flash" data="http://d1.scribdassets.com/ScribdViewer.swf"; style="outline:none;" > <param name="movie" value="http://d1.scribdassets.com/ScribdViewer.swf";> <param name="wmode" value="opaque"> <param name="bgcolor" value="#ffffff"> <param name="allowFullScreen" value="true"> <param name="allowScriptAccess" value="always"> <param name="FlashVars" value="document_id=30552&access_key=8gu5a2firfg4u&page=1&viewMode=list"> <embed id="doc_419953862916615" name="doc_419953862916615" src="http://d1.scribdassets.com/ScribdViewer.swf?document_id=30552&access_key=8gu5a2firfg4u&page=1&viewMode=list"; type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" height="600" width="100%" wmode="opaque" bgcolor="#ffffff"></embed> </object>

>I do not know the author, but it seems to me a strong
>counterexample to the Pythagorean Proposition:

You mean a counterexample to Elisha Loomis' opinion?

Yeap, fine.

sorry forgot to change the html code:

I found the following at http://www.scribd.com/doc/30552/A-Calculus-Proof-of-the-Pythagorean-Theorem

I do not know the author, but it seems to me a strong counterexample to the Pythagorean Proposition:

A Calculus Proof of the Pythagorean Theorem

OK apparently the html is not working, or I am missing something but the link still works... could this be proof #89?

By the way I have to mention again I do not know the author of this page, but he seems to have gone to great lengths to defend his use of Calculus...

1. I have two calculus proofs on my page.
2. I have no patience with your link. He used calculus to argue that

F(x,y) ≥ 0

while it is obvious from the definition.

I am not wedded to the Pythagorean theorem or to its proofs. Sometimes I err in my selections, perhaps, even often so, but what I am on lookout for is elegance not a refutation of Elisha Loomis' opinions. So, no, this is not going to be proof #89.

>1. I have two calculus proofs on my page.

Yes, sir. I realize that. I did not mean to sound like you were lock-in-step with Loomis.

>2. I have no patience with your link. He used calculus to
>argue that
>
>F(x,y) ≥ 0
>
>while it is obvious from the definition.

I need help on this. Did you mean that the statement was unnecessary, or that it depends on the PT and creates a circular argument?

>
>I am not wedded to the Pythagorean theorem or to its proofs.
>Sometimes I err in my selections, perhaps, even often so,
>but what I am on lookout for is elegance not a refutation of
>Elisha Loomis' opinions. So, no, this is not going to be
>proof #89.

Sorry, I jumped the gun on this a little and was wrong to suggest that you post this to your page as proof #89. I apologize if I offended you. Ironically, I am still "wedded" to my own Calculus proof and hope somehow to argue its validity. I suppose I am stubborn in that regard. It was my intention to look at this link as an improvement somewhat in my own thinking.

I am still having a hard time with the reasoning behind why my own calculus proof is circular. I suppose I am blind to some big assumptions I made on that, or else I am ignorant of the circularity somewhere. Rest assured, I am trying.

Also, I did post that proof on mathforum... And the discussion there got me to thinking that I should not assume that slope of a line can be gained apart from the PT. Am I headed in the right direction?

Again you have been very kind to respond to my barrage of posts recently. Thanks for your correspondence and commentary.

>>2. I have no patience with your link. He used calculus to
>>argue that
>>
>>F(x,y) ¡Ư 0
>>
>>while it is obvious from the definition.
>
>I need help on this. Did you mean that the statement was
>unnecessary, or that it depends on the PT and creates a
>circular argument?

No, it is exactly as I wrote. He defined F(x, y) which is by defintion is not negative and then wasted a page proving that it is so by using calculus. There is not circularity but a waste.

>Also, I did post that proof on mathforum... And the
>discussion there got me to thinking that I should not assume
>that slope of a line can be gained apart from the PT.

Just continue the discussion there.

HTML works fine, except you should use square and not angular brackets.

This appears to have come from a book entitled "The Pythagorean Theorem:
Crown Jewel of Mathematics"

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John C. Sparks

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