More Presidents:
Yes, but which President is credited for having come up with an original proof of the Pythagorean Theorem?
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More Presidents:
Yes, but which President is credited for having come up with an original proof of the Pythagorean Theorem? 
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Proof
QuickTime Proof
That's my problem with it.
"Secondly, arguing the areas of the figures from analytic geometry (the essential source of the formulae)...."
Actually, no. These areas can be found in an entirely coordinatefree (nonanalytic) context, so there's no danger of a hidden use of a "distance formula."
It's easy to show that the area of a triangle is 1/2 the area of a circumscribing rectangle, and a trapezoid is in general just the sum of a rectangle and at most two triangles.
But I share your dislike of this proof, in spite of having animated it....
I'm wrong about that, come to think of it. Anyway, this special trapezoid is luckily just the union of one rectangle and one triangle....
I agree that they don't make congressmen like that anymore. Some of us were pretty good at math in high school and college but never came up with a proof for anything. I never learned to write Greek or Latin with either hand. The old guys got a much better education than I did in the 40's and 50's and MUCH better than today.
If I had to guess (assuming that fluent means fluent and not the pissant phrasebook stuff some of them affect), I would say either FDR or Hoover. George HW Bush and Nixon are maybes, but I don't recall their fluency in a foreign language.
Does anyone know the answer?
I first ran across Garfield's proof about ten years ago in a little book called The Most Beautiful Mathematical Formulas. I was impressed by the relative clarity and brevity of the proof then and still am now. Garfield's proof of the Pythagorean Theorem may be the most elegant I've ever seen. I majored in math and have a pretty good background in geometry: I've waded through a good bit of Euclid's Elements and Hilbert's analysis and reformulation. Is some of the prejudice against Garfield's proof just because it is partially algebraic and hence not in the spirit of Euclid or does it derive from some latent prejudice against a succesful Republican politician of the gilded age?
I remember his pistols and saber from the civil war being on display.
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I think the biggest prejudice is the one that John Armstrong mentioned, above, that it's really just a needless complication of the more famous, much older, and more elegant "three squares" proof. The algebraic part is merely a convenience. It could easily be rewritten completely in terms of Euclid's postulates, but that would make it a lot harder for us modern folks (meaning Garfield, as well) to follow.
But it still seems to me to be a much more productive use of chamber time in the House of Representatives than what we currently get from our legislators.
I think TR was the last American president who could converse in a living foreign language. It's embarrassing to be associated with the American flag. I don't think TR was circumcised.
Perhaps if we elected more Congressmen and Presidents who are graduates of the nation's finest liberal arts college, rather than those educated in the stifling atmosphere of the Ivy League...
A PhD in science used to require literacy (at least at the level of reading journal articles) in two second languages and the ability to converse in one of them.
I know this because my Dad was quite proud of his (awful) German. He was a Physics PhD from the University of Colorado. Reading journal articles in any of the Romance languages isn't all that hard, given time and a dictionary.
I believe that this requirement is dropped now. English fluency appears to be the de facto standard in the sciences.
I wonder how long this special case of the Pythagorean Theorem had been proved prior to the first proof of the fullblown Pythagorean Theorem. It also may be that either the special case or the general result were known empirically before they were actually proved.
An interesting historical question, methinks.