Pythagorean Theorem is Wrong
Rod Reynolds
Rod Reynolds
http://aspoonfulweighsaton.blogspot.com/2006/04/great-hoax_21.html
Keith A. Lewis
The Pythagorean Theorem has been proven. If you want to refute it, the
burden of proof is on you, not on those who accept the previous proofs.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
fishfry
<22164990.1159039116...@nitrogen.mathforum.org>,
Rod Reynolds <rdrd...@hotmail.com> wrote:
> I've shown it in my blog
> http://aspoonfulweighsaton.blogspot.com/
Pythagoras is going to be pythed.
Rod Reynolds
The Ghost In The Machine
<rdrd...@hotmail.com>
wrote
on Sat, 23 Sep 2006 15:18:06 EDT
<22164990.1159039116...@nitrogen.mathforum.org>:
You are extremely confused. How do 10, 20, and 25 make
a right triangle, on a standard flat surface?
Best I can do there is 15, 20, 25, which do indeed make a right
triangle, as they are multiples of the rather well-known right triangle
formed by sides 3, 4, and 5.
If one constructs a triangle from 2, 4, and 5, one can use the
following
http://mathforum.org/library/drmath/view/53931.html
to get the angles A, B, and C.
s = (2+4+5)/2 = 11/2
K = sqrt(11/2 * 7/2 * 3/2 * 1/2) = (1/4) * sqrt(231)
sin(A) = 2K/(b*c) = sqrt(231)/(2*4*5) = 0.37996710
sin(B) = 2K/(a*c) = sqrt(231)/(2*2*5) = 0.75993421
sin(C) = 2K/(a*b) = sqrt(231)/(2*2*4) = 0.94991776
It is somewhat difficult to tell given solely this formula
if the angles are acute or if one of them is obtuse, but
it's clear that this is not a right triangle (sin 90 = 1).
Contrast this to the calculation given a=3, b=4, and c=5,
the more or less standard "first Pythagorean triplet".
s = (3+4+5)/2 = 6
K = sqrt(6*3*2*1) = 6
sin(A) = 2K/(4*5) = 3/5
sin(B) = 2K/(3*5) = 4/5
sin(C) = 2K/(3*4) = 1
therefore C is a right angle, obviously.
Now, if you want to play with great circles, a number
of weird triangles are possible. The simplest one I can
think of is an equilateral triangle in which *all* angles
are right angles, by taking 1/4 of the equator and then
drawing great circles to one of the poles; all arcs are
the same length.
I can generate an infinite number of isosceles triangles
in which two of the angles are right angles by varying
the length of the equatorial arc.
I'd have to do some work regarding scalene variants.
--
#191, ewi...@earthlink.net
Windows Vista. Because it's time to refresh your hardware. Trust us.
Rod Reynolds
Stephen Montgomery-Smith
> How do you feel about the other article I presented? You know, the one about 437 not existing?
I thought it was a better article than the other one.
Tim Peters
> How do you feel about the other article I presented? You know,
> the one about 437 not existing?
I'm outraged that this has been suppressed in North America -- and I wrote a
computer program that verified the claim. I had noticed before that 437
seemed to be systematically missing in output, but never suspected how deep
the problem was. I figured it was just another Pentium bug.
http://aspoonfulweighsaton.blogspot.com/2006/04/great-hoax_21.html
Good work debunking that Pythagoras fellow, too! I can't abide blowhards
hiding behind pseudonyms either :-)
Bob Kolker
> I've shown it in my blog
> http://aspoonfulweighsaton.blogspot.com/
The pythagorean theorem has over 500 known proofs. You clearly have made
a mistake.
Bob Kolker
Lee Rudolph
Ah, but what about that gap between the 436th and 438th proof, eh? Eh???
Lee Rudolph
Rod Reynolds
Also, I'm not going to go through 500 proofs when I've already shown that they're wrong.
Gib Bogle
It was very nice, but it would have helped if they'd at least sketched
out the proof. I know that mere mortals can't expect to understand
fully Hawking's thinking, but we can at least have the illusion of
understanding.
Bob Kolker
> That's just your opinion. The neat thing about math is that there is no "right answer".
>
> Also, I'm not going to go through 500 proofs when I've already shown that they're wrong.
You haven't. What you wrote in your blog is gibberish.
Bob Kolker
Rod Reynolds
Gene Ward Smith
The Ghost In The Machine wrote:
> sin(A) = 2K/(b*c) = sqrt(231)/(2*4*5) = 0.37996710
> sin(B) = 2K/(a*c) = sqrt(231)/(2*2*5) = 0.75993421
> sin(C) = 2K/(a*b) = sqrt(231)/(2*2*4) = 0.94991776
>
> It is somewhat difficult to tell given solely this formula
> if the angles are acute or if one of them is obtuse, but
> it's clear that this is not a right triangle (sin 90 = 1).
That's lame. Why not use the law of cosines?
.
Stephen Montgomery-Smith
Now this is definitely a man without a sense of humor!!!!
By the way, Mr. Spoon - I once did try your advice on on this same web
pages "Yes, as a matter of fact I am carrying a bomb. It's in my
backpack." As it happens I was taking a wheelchair bound man to an
airport - he had already told me that he had missed countless flights
because some idiot made a joke about guns in his wheelchair - and like
an unthinking idiot I actually made that joke at airport security. This
was all before 9/11, and it was a small regional airport, so the airport
security had grace upon us, but it was a very tense moment.
Stephen
The Ghost In The Machine
<genewa...@gmail.com>
wrote
on 23 Sep 2006 19:26:28 -0700
<1159064788....@e3g2000cwe.googlegroups.com>:
Such is indeed possible, I suppose. I'm not that familiar
with analytical geometry.
http://hyperphysics.phy-astr.gsu.edu/hbase/lcos.html
indicates that the Law of Cosines is the expression
c^2 = a^2 + b^2 - 2ab*cos C.
and I for one would surmise so are the rotations:
a^2 = b^2 + c^2 - 2bc*cos A
b^2 = c^2 + a^2 - 2ca*cos B
So
5^2 = 2^2 + 4^2 - 2*2*4*cos C
cos C = (5^2 - 2^2 - 4^2) / (2*2*4) = 0.3125
It turns out .94991776^2 + 0.3125^2 = 1, or near enough, so
that's a useful check.
Gib Bogle
Mathematicians just lie and lie and lie.
N. Silver
> I've shown it in my blog
> http://aspoonfulweighsaton.blogspot.com/
You are claiming that 10, 20, 25 are lengths
of sides of a right triangle. If this is the case,
then the Pythagorean Theorem fails for this
particular triangle. Is that right? (Pun intended.)
We can construct a 30 by 30 square as follows.
A
________20_______|___10____
| |
10 | |
| | 20
D_| |
| |
| |
| |--- B
20 | |
| | 10
|___10____|______20________|
C
Connect points on the square with line segments: AB, BC, CD, AD.
The area of the big square is 900 square units. The areas of each
of the right triangles is 100 square units, giving 400 square units for
the four triangles. Subtracting we get the area of the smaller square,
inside the big square, which is 900 - 400 = 500. Then each hypotenuse
has length = sqrt(500) which is different than 25. Therefore, the triangle
10, 20, 25 is not a right triangle.
Proginoskes
Rod Reynolds wrote:
> Also, I discuss the recent finding that 437 may not exist.
>
> http://aspoonfulweighsaton.blogspot.com/2006/04/great-hoax_21.html
Wow. Someone more clueless than James Harris. Who'd-a thunk it? And on
Usenet, no less.
--- Christopher Heckman
Virgil
Gib Bogle <bo...@ihug.too.much.spam.co.nz> wrote:
Not quite.
What they actually do is "Why?" and "Why?" and "Why?"
And Gib Bogle is boggled trying to answer.
Rod Reynolds
But it does sound like an interesting situation! Now all you have to do is start diagnosing people with fatal conditions. Good luck.
Stephen Montgomery-Smith
But you are trying to provide a proof of Pythagorus by providing a proof
of Pythagorus. This is a circular argument, particularly in view of the
OP's assertion that all of the proofs of Pythagorus are wrong.
Rod Reynolds
It is mind boggling how stupid some people can be. "I'm right, because of the following reasons". Well, I've already told you that I'm not going to believe your reasons. Jeez...
Stephen Montgomery-Smith
Yes, that is a much more direct counter-argument.
Virgil
<13470000.1159105456...@nitrogen.mathforum.org>,
Rod Reynolds <rdrd...@hotmail.com> wrote:
> It is mind boggling how stupid some people can be. "I'm right, because of
> the following reasons". Well, I've already told you that I'm not going to
> believe your reasons. Jeez...
Then we are equally free to ignore your reasons.
And as there are a lot more of us,...
Rod Reynolds
> <13470000.1159105456...@nitrogen.math
> forum.org>,
> Rod Reynolds <rdrd...@hotmail.com> wrote:
>
> > It is mind boggling how stupid some people can be.
> "I'm right, because of
> > the following reasons". Well, I've already told
> you that I'm not going to
> > believe your reasons. Jeez...
>
> Then we are equally free to ignore your reasons.
>
> And as there are a lot more of us,...
I am having a very tough time understanding how you, and many here, are oblivious to what is going on.
Virgil
<20698719.1159117040...@nitrogen.mathforum.org>,
Rod Reynolds <rdrd...@hotmail.com> wrote:
> > In article
> > <13470000.1159105456...@nitrogen.math
> > forum.org>,
> > Rod Reynolds <rdrd...@hotmail.com> wrote:
> >
> > > It is mind boggling how stupid some people can be.
> > "I'm right, because of
> > > the following reasons". Well, I've already told
> > you that I'm not going to
> > > believe your reasons. Jeez...
> >
> > Then we are equally free to ignore your reasons.
> >
> > And as there are a lot more of us,...
>
>
>
> I am having a very tough time understanding how you, and many here, are
> oblivious to what is going on.
We, on the other hand, have no understanding of your nonsense at all.
Since there are many proofs of the truth of the Pythagorean theorem
which you have not been able to fault, you are in effect saying that
mathematics contains contradictions.
In which case, the Pythagorean theorem, and anything else, will be both
true and false.
So either your theorem is false because its alleged proof is faulty , or
it is false because every statement in mathematics is false.
In either case, you lose.
Marshall
>
> I am having a very tough time understanding how you, and many
> here, are oblivious to what is going on.
Hey, I tried the same thing a few weeks back and got about
the same response. The crankery on sci.math just *begs*
for parody, but as best I can tell, many of the regulars have
a hard time recognizing it. I think they see so much awful
crap so often that the line between parody and insanity
is no longer apparent.
Marshall
PS. I enjoyed your blog.
Rod Reynolds
> So either your theorem is false because its alleged
> proof is faulty , or
> it is false because every statement in mathematics is
> false.
>
> In either case, you lose.
I am more likely to agree with the second statement. This is because I have reported in the past that pretty much the entire mathematical enterprise lies in ruins, due to the nonexistence of a number, number 437. This is the second article I presented. I don't think you've read it yet. So, I'll link to it again.
http://aspoonfulweighsaton.blogspot.com/2006/04/great-hoax_21.html
And, if after reading that, you are still confused, I recommend reading [url=http://en.wikipedia.org/wiki/Joke]this article.[/url]
Rod Reynolds
Thanks, I'm glad you liked it.
I wasn't sure if I should look down upon these people. Then I thought what you just pointed out, that it probably means that there are actually people as ignorant as what I'm pretending to be who post here, so there ability to detect parody has gone out the window.
skuesey
Guess what? I can also think of three numbers that don't fit
Pythagoras' theorum - 1, 2 and 3.
Since I believe Pythagorus' theorum to be right, I believe (sorry, I
know) that you can't draw a right angled triangle with sides of length
1, 2 and 3 units. Since you obviously think Pythagoras' theorum is
wrong, would you like to draw me such a triangle to prove your point?
The burden of proof is now on you.
skuesey.
Stephen Montgomery-Smith
I felt that it was so obvious that your web site was a parody, that I
was frankly rather surprised at the extent to which people took offense.
And if they didn't see it from your web site, your replies made it
totally obvious.
Personally I found your humor to be rather cute, and it brought a smile
to my lips.
Thanks, Stephen
Rod Reynolds
Rod Reynolds
I don't know who James Harris is, but I have a hard time believing that either him or I are the most clueless ones here.
Virgil
<22289616.1159121789...@nitrogen.mathforum.org>,
Rod Reynolds <rdrd...@hotmail.com> wrote:
> >
> > So either your theorem is false because its alleged
> > proof is faulty , or
> > it is false because every statement in mathematics is
> > false.
> >
> > In either case, you lose.
>
> I am more likely to agree with the second statement.
Your agreement or disagreement with anything is irrelevant.
> This is because I have
> reported in the past that pretty much the entire mathematical enterprise lies
> in ruins, due to the nonexistence of a number, number 437.
As a reporter, you might make janitor.
Try (21 - 2)*(21 + 2) .
Bob Kolker
Yoo hoo? In a triangle the sum of the lengths of two sides must exceed
the length of the third. 1 + 2 does not exceed three so there is not
1,2,3 triangle.
Bob Kolker
Rod Reynolds
Virgil
<2498448.11591302715...@nitrogen.mathforum.org>,
Rod Reynolds <rdrd...@hotmail.com> wrote:
> And did you check out the final link I gave you?
Why bother, when you have already told us it contains falsehoods?
Gene Ward Smith
Rod Reynolds wrote:
> I wasn't sure if I should look down upon these people. Then I thought what you just pointed out, that it probably means that there are actually people as ignorant as what I'm pretending to be who post here, so there ability to detect parody has gone out the window.
You've certainly discovered that it's difficult to parody crank
mathematics.
Aatu Koskensilta
> Rod Reynolds <rdrd...@hotmail.com> wrote:
>> And did you check out the final link I gave you?
>
> Why bother, when you have already told us it contains falsehoods?
Don't be silly; Reynolds didn't claim the Wikipedia article on jokes
contains falsehoods.
--
Aatu Koskensilta (aatu.kos...@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Marshall
I don't know that I agree with that interpretation. It may be
rather than those who are steeped in crankiness lose
something of their sense of humor, or at the very least
their ability to detect parody. It seems the less of sci.math
one has read, the easier it is to spot the parody.
Marshall
Rod Reynolds
I think you're right, as I can attest to the fact that it is very easy to write this stuff. I guess that's why I do it, because of the high "enjoyment:work" ratio. I think it may be wise for me to not stick around, as I am rather fond of my sense of humour.
Tonico
Rod Reynolds ha escrito:
> > Gene Ward Smith wrote:
> > > Rod Reynolds wrote:
> > >
> > > > I wasn't sure if I should look down upon these
> > people. Then I thought what you just pointed out,
> > that it probably means that there are actually people
> > as ignorant as what I'm pretending to be who post
> > here, so there ability to detect parody has gone out
> > the window.
********************************************************
Hi all:
Since the article about the pythagorean theorem being screwed
was pretty funny and actual cranks/trolls have the same sense of
humour as 3 pounds of dry garlic, I knew from the beginning this must
be a
a joke. The article about the sad discovery that 437 doesn't
actually exist just confirmed it.
I find ashtonishing the number of people that, apparently,
believed the above articles were serious ones...unless they
also were playing as well and I didn't find out.
Was a nice thread!
Tonio
Stephen Montgomery-Smith
> I think you're right, as I can attest to the fact that it is very easy to write this stuff. I guess that's why I do it, because of the high "enjoyment:work" ratio. I think it may be wise for me to not stick around, as I am rather fond of my sense of humour.
1. I also enjoy your sense of humor. I find your humor to be gentle
and decent.
2. I also have the same weakness as you - I am too fond of my sense of
humor.
3. Please stick around. I will enjoy your future posts.
Thanks, Stephen