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Author Topic: What do you think of this proof of the Pythagorean Theorem?  (Read 2866 times)

Offline PmbPhy

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We all use the Pythagorean Theorem a great deal in math and physics. In case you've never seen a proof of it I created one and placed it on my website for all to read. It's at
http://home.comcast.net/~peter.m.brown/math_phy/pythagorean_theorem.htm

I'm curious. I learned this several decades ago. I was wondering if anybody has ever seen this proof before? Thanks.
« Last Edit: 25/06/2014 11:10:22 by Georgia »


 

Offline lightarrow

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We all use the Pythagorean Theorem a great deal in math and physics. In case you've never seen a proof of it I created one and placed it on my website for all to read. It's at
http://home.comcast.net/~peter.m.brown/math_phy/pythagorean_theorem.htm

I'm curious. I learned this several decades ago. I was wondering if anybody has ever seen this proof before? Thanks.
Very interesting, I didn't know it. It's more simple to remember than the Euclide relations I studied to prove the theorem.

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lightarrow
 

Offline jccc

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Yes, very simple beautiful. Who taught you that? hahahaha
 

Offline PmbPhy

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Quote from: jccc
Yes, very simple beautiful. Who taught you that? hahahaha
What's so funny about it? I learned it in my freshman physics class close to 30 years go. Since I've never seen anybody mention it since then I decided to put it online. Especially it since it seems to have been in question by a member who started a thread in New Theories sub forum who claimed that the time dilation formula derivation was wrong. His counter argument included the Pythagorean forum. The time dilation proof is the one on my website at
http://home.comcast.net/~peter.m.brown/sr/time_dilation.htm
 

Offline alancalverd

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My father taught it to me 60 years ago. He said it was known as the Chinese proof and was reputed to be about a thousand years older than Pythagoras.
 

Offline percepts

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I saw another which is simpler to understand IMO. The language used to state the theorem is critical to intuitive understanding.

1. The square of the hypotenuse is equal to the sum of the squares of the opposite two sides. (the usual misquoted theorem)

2. The square ON the hypotenuse is equal to the sum of the squares ON the opposite two sides

that little change from OF to ON makes it much more obvious. You just draw a square on each side using the sides length and compare the area of the square ON the hypotenuse against the sum of the square areas ON the opposite two sides.

 

Offline alancalverd

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That's a sound experimental observation for reasonably near-isosceles triangles, but it isn't a valid proof for all possible right-angled triangles. And it's excessively complicated and difficult to do. Why not just measure a, b and c and calculate the sum of squares?

The strength of the classic Pythagoras proof is that it demonstrates that the theorem holds for all rightangled triangles and only rightangled triangles, with no allowance required for experimental error. You can therefore use it for life-and-death applications like navigation and architecture, and presume that if a2 = b2 + c2 then b and c are orthogonal.The Chinese proof is regarded as rather weak by mathematicians because it leans on symmetry and doesn't exclude the possibility of the equation holding for other shapes. 
« Last Edit: 27/06/2014 21:52:23 by alancalverd »
 

Offline jccc

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I kind of remember a story. The guy first solved it was a Greek, he killed a cow to celebrate, and told his students not to tell the secret to others, otherwise, he'll kill them.

Assume that's true, so Pete, may I use your proof to show off with peace?
 

Offline PmbPhy

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Quote from: alancalverd
Why not just measure a, b and c and calculate the sum of squares?
For two reasons (1) you can't measure lengths with infinite precision so you'd be unable to claim it was exact and (2) you'd have to do it for all possible variations of a, b and c. One doesn't go to the lab and take measurements when a proof is as simple as the one I gave.

Quote from: alancalverd
The strength of the classic Pythagoras proof is that it demonstrates that the theorem holds for all rightangled triangles and only rightangled triangles, with no allowance required for experimental error.
There is no experimental error in math problems. For other triangless other than right triangles there is another relation. This one is for the special case of right triangles. I posted it because in practice it's used much more than the general case. Besides, the general triangle can be resolved into two right triangles.
« Last Edit: 28/06/2014 06:10:17 by PmbPhy »
 

Offline PmbPhy

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Quote from: jccc
... may I use your proof to show off with peace?
You know, don't you, that you don't need to ask me to show what's on my website to others? In any case after I created that page I did some searching and found that its a well-known derivation anyway. It's on Wikipedia if I recall.
 

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