Disproof of Pythagorean Theorem

2007 October 10
by jd2718

Go, run, look for yourself:

[_MG_7916.jpg]

[_MG_7917.jpg]

Richard Mason watches mathematical certainty slip away.

This certainly spins that Greek theory on its head.

from → Puzzles, mathematics

9 Responses leave one →
  1. 2007 October 10
    professore permalink

    Everybody knows that physicists don’t know mathematics. :-)

    Reply
  2. 2007 October 10
    vlorbik permalink

    fyi: i can’t see the graphic in your post
    (just an error message indicating that
    SOMETHING.jpg should have been there).

    great find!

    Reply
  3. 2007 October 10
    Myrtle Hocklemeier permalink

    That was priceless.

    Maybe the museum knowingly put that exhibit out there to get a conversation started on the topic of “Why empirical experiments don’t constitute mathematical justification.” Is that possible or am I being overly charitable?

    A comment similar to the one that was posted above was made at my house as well. I had to convince my husband that the original blogger was being sarcastic.

    Reply
  4. 2007 October 10
    jd2718 permalink

    vlorbik,

    it’s a mess here, too. At home it showed up nice. I’ll take a look this evening.

    Reply
  5. 2007 October 11
    Jackie permalink

    I see the graphic (firefox on a mac). Great find – thanks!

    Reply
  6. 2007 October 11
    jd2718 permalink

    Looks fine to me. I commented on the blog:

    Maybe there is liquid hiding behind the triangle? So in the first picture, there could be more than meets the eye, and in the third, the extra water settles in a thin strip, mostly hidden behind the triangle, but with those two extensions to the left and right.

    Perhaps the Theorem is not broken, but it’s just sprung a leak.

    Reply
  7. 2007 October 12
    Jose permalink

    I like this. And it’s cool, though I’m not sure if the densities are on point, just like many of the commenters mentioned. Nonetheless, it’s a fun look at an age-old theorem.

    Reply
  8. 2007 December 2
    Richard Mason permalink

    Hi Jonathan, I just belatedly noted your comment on my blog re the botched Pythagoras museum demo.

    The source of the problem was not blatantly obvious from visual inspection of the apparatus. But I doubt that there was a *significant* amount of fluid hiding behind the triangle. That would seem to require *total* cluelessness by the exhibit constructors.

    More likely, the constructors knew basically what they were trying to do, and were reasonably skilled in carpentry, but did not consider the required precision for the uniform depth of the tanks (depth normal to the plane of the triangle). Since the tanks were not very deep (~1 cm), a variation in depth that might seem quite small in absolute distance (~1 mm) could produce a big percentage error in volume and ruin the demo.

    The same one-millimeter construction error in any of the other dimensions of the apparatus would have made much less difference to the volume and thus less fluid overspill, probably not enough to spoil the demo.

    Perhaps this itself is an interesting real-world lesson in mathematics.

    Reply

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