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Back in 1876, then US Congressman James Garfield came up with a "new" proof
of the Pythagorean Theorem, based on the area of a trapezoid. Four years
later, he would be elected President, and a few months after assuming
office he was assassinated. There is no evidence that his proof of the
Pythagorean Theorem had anything to do with the assassination.
In commemoration of the fact that we had a US President, once, who created
an original mathematical proof, and in tacit recognition that we probably
never will again, I made a QuickTime movie demonstrating the proof.
Because it's QuickTime, and because it's about 6 meg's, I've just posted a
link:
http://www.mnwest.edu/website/dmatthews/explorations/garfieldfull01.mov
The astute observer will note that it's not a very remarkable proof,
basically just half of the ancient "square in a square" proof.
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From: Thibaut Jonckheere
Subject: Re: Garfield's Proof of the Pythagorean Theorem
Date: 1 Feb 2006 15:44:48
Message: <43e11dc0$1@news.povray.org>
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Dave Matthews wrote:
> Back in 1876, then US Congressman James Garfield came up with a "new" proof
> of the Pythagorean Theorem, based on the area of a trapezoid. Four years
> later, he would be elected President, and a few months after assuming
> office he was assassinated. There is no evidence that his proof of the
> Pythagorean Theorem had anything to do with the assassination.
>
I have a vague remembrance from an article I read some time ago, that
this guy was also able to write with one hand in latin, and at the same
time with the other hand in greek...
The animation is nice, but I find it goes and moves a bit too quickly to
allow to really understand the proof at first view.
Thibaut
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Thibaut Jonckheere <tua### [at] yahoo fr> wrote:
> I have a vague remembrance from an article I read some time ago, that
> this guy was also able to write with one hand in latin, and at the same
> time with the other hand in greek...
Yes, I recall that also, and found a mention of it here:
http://www.mind-course.com/ambi.html
> The animation is nice, but I find it goes and moves a bit too quickly to
> allow to really understand the proof at first view.
Thanks, and I agree it's too fast. Adding frames to slow it down makes it
huge. I'm wondering if there's a more efficient compression method that
doesn't fuzz up the image too much. I like to keep the size large (640 x
480), but it's already a bit of a waste of space at 6 megs....
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From: Zeger Knaepen
Subject: Re: Garfield's Proof of the Pythagorean Theorem
Date: 2 Feb 2006 10:07:57
Message: <43e2204d$1@news.povray.org>
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"Dave Matthews" <dav### [at] mnwestedu> wrote in message
news:web.43e20bb2d2cab98a8c7259570@news.povray.org...
> Thanks, and I agree it's too fast. Adding frames to slow it down
makes it
> huge. I'm wondering if there's a more efficient compression method
that
> doesn't fuzz up the image too much. I like to keep the size large
(640 x
> 480), but it's already a bit of a waste of space at 6 megs....
lower framerate? :)
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From: "Jérôme M. Berger"
Subject: Re: Garfield's Proof of the Pythagorean Theorem
Date: 2 Feb 2006 13:41:30
Message: <43e2525a$1@news.povray.org>
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-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
Dave Matthews wrote:
> Thanks, and I agree it's too fast. Adding frames to slow it down makes it
> huge. I'm wondering if there's a more efficient compression method that
> doesn't fuzz up the image too much. I like to keep the size large (640 x
> 480), but it's already a bit of a waste of space at 6 megs....
>
DivX? Here's a 630k version of yours without fuzz:
http://jeberger.free.fr/tmp/garfieldfull.avi
Or you could go for MPEG1. It'll be bigger than DivX, but still
much smaller than your MJPEG for the same quality...
Jerome
- --
******************************
* Jerome M. Berger *
* mailto:jeb### [at] freefr *
* http://jeberger.free.fr/ *
******************************
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"Zeger Knaepen" <zeg### [at] povplacecom> wrote:
> lower framerate? :)
I'm already down to 10 frames per second - I think the next step is still
shots.
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=?ISO-8859-1?Q?=22J=E9r=F4me_M=2E_Berger=22?= <jeb### [at] freefr> wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Dave Matthews wrote:
> DivX? Here's a 630k version of yours without fuzz:
> http://jeberger.free.fr/tmp/garfieldfull.avi
That's fantastic. What did you use to convert it? 630 k makes it
reasonable.
Dave
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From: "Jérôme M. Berger"
Subject: Re: Garfield's Proof of the Pythagorean Theorem
Date: 3 Feb 2006 15:44:09
Message: <43e3c099@news.povray.org>
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-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
Dave Matthews wrote:
> =?ISO-8859-1?Q?=22J=E9r=F4me_M=2E_Berger=22?= <jeb### [at] freefr> wrote:
>
>>-----BEGIN PGP SIGNED MESSAGE-----
>>Hash: SHA1
>>
>>Dave Matthews wrote:
>> DivX? Here's a 630k version of yours without fuzz:
>>http://jeberger.free.fr/tmp/garfieldfull.avi
>
>
> That's fantastic. What did you use to convert it? 630 k makes it
> reasonable.
>
I used mencoder on linux with the XviD codec and two-pass encoding.
The actual command lines were:
mencoder -ovc xvid -xvidencopts
vhq=4:max_bframes=2:qpel:gmc:lumi_mask:autoaspect:psnr:bitrate=256:pass=1
- -nosound -o garfieldfull.avi garfieldfull01.mov
mencoder -ovc xvid -xvidencopts
vhq=4:max_bframes=2:qpel:gmc:lumi_mask:autoaspect:psnr:bitrate=256:pass=2
- -nosound -o garfieldfull.avi garfieldfull01.mov
Since you're on windows, you might want to look here for the XviD
codec:
http://www.zdnet.fr/telecharger/windows/fiche/0,39021313,11010875s,00.htm
I don't know what frontend you use to generate your video, but I
would recommend VirtualDub:
http://www.virtualdub.org/
- --
******************************
* Jerome M. Berger *
* mailto:jeb### [at] freefr *
* http://jeberger.free.fr/ *
******************************
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=?ISO-8859-1?Q?=22J=E9r=F4me_M=2E_Berger=22?= <jeb### [at] freefr> wrote:
> Since you're on windows, you might want to look here for the XviD
> codec:
> http://www.zdnet.fr/telecharger/windows/fiche/0,39021313,11010875s,00.htm
>
> I don't know what frontend you use to generate your video, but I
> would recommend VirtualDub:
> http://www.virtualdub.org/
>
Thanks. VirtualDub is really nice, and using the XviD codec and VirtualDub,
I've gotten it down to about 1.45 megs -- once I figure out the 2-pass
trick, maybe I can compress it even more.
(I was just using QuickTime Pro, but I always prefer to find open source
alternatives.)
Dave Matthews
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=?ISO-8859-1?Q?=22J=E9r=F4me_M=2E_Berger=22?= <jeb### [at] freefr> wrote:
> I don't know what frontend you use to generate your video, but I
> would recommend VirtualDub:
> http://www.virtualdub.org/
>
And adjusting the target bitrate down to 256 got me in under 600 k. Thanks
again! I teach on-line classes, and now I can post up decent
demonstrations that won't take them an hour to download on dial-up
connections.
Dave Matthews
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