Pythagorean theorem fail

Richard over at Tales of the Golem; or, the Modern Epimetheus claims to have “convincing experimental disproof of Pythagoras’s theorem!”

pythagorean disproof

In the first picture, the water covers the area a^2+b^2 while in the third picture, it covers an area larger than that of c^2. Thus, a^2+b^2 > c^2. Guess all of mathematics was wrong! 😉

** Note: Some posts on Math-Fail are user-submitted and NOT verified by the admin of the site before publication. If you find this post to be distasteful, non-math related, ?or something worse?, then definitely leave a comment letting me know. Thanks very much! Mike **

1 Star2 Stars3 Stars4 Stars5 Stars (2.33 from 3 votes)


  1. That`s impossible!
    Only explanation – he made those squares wrong!

    Thumb up 0 Thumb down 0

  2. Bryan Lee Williams

    He did not make the squares wrong. He made an experiment that doesn’t mean anything.
    Because the triangle is not translucent, you don’t see the fluid behind it which it obviously is.
    The area of the fluid for this experiment to be able to cover both the a^2 and b^2 areas is actually
    a^2 + b^2 plus ab/2.
    So when filling the c^2 area, there is ab/2 fliud left over.

    Thumb up 2 Thumb down 0

  3. Not quite, in the second picture, the water levels don’t add up, so they can’t be connected.
    It’s more likely that they messed up when building that thing, like having the big square be slightly thinner than the other two.yyy

    Thumb up 0 Thumb down 0

  4. It almost adds up. He probably has a pivot through the centerpiece behind the triangle.

    Thumb up 0 Thumb down 0

  5. The depth isn’t constant, thus this experiment is rigged.
    You can see this easily in the second image, the b square is much thinner in volume than the a square. (Most likely, the a is thicker than either of the other two.)
    Look at the bubbles. In a there is some depth as the water surrounds the bubble. But in b, there is no visible depth because the container is so thin the bubble takes the entire depth.
    Also, look at the discharge in the c tank. There is a much more violent stream into the side from the a in relation to the b, indicating a higher PSI, which means there is more depth in a.

    Thumb up 0 Thumb down 0

  6. You are all a litle bit wrong and maybe a little bit right – the problem is; you don’t understand the theorem – The square of the hypotenuse, etc is the AREA, not the VOLUME!!!!!!!!!! As soon as you add thickness you must adjust the theorem to the VOLUME on the hyp. is equal to the sum of the VOLUMES of the other 2 sides (and Pytagoras did say that, as well!!!!)

    Thumb up 2 Thumb down 1

  7. Dave, you are correct.
    Also, nice scarf on that guy. Where can I buy one?

    Thumb up 0 Thumb down 0

  8. Dave, settle down. We’ll do it by volume if you like:
    h_1*a^2 + h_2*b^2 = h_3*c^2
    Assuming the depths (h) are equal, the above expression simplifies to the Pythagorean Theorem we know and love. The trouble is, they don’t, so we can’t.

    Thumb up 0 Thumb down 0

  9. The thing is right – nobody before ever checked this and the world is now a very different place! Pythag was an A/hole.

    Thumb up 1 Thumb down 0

  10. I’m pretty sure there was some liquid inside the triangle (or even outside both the triangle and the squares) to keep the liquid inside the smaller squares in place.

    Besides, there’s the simple fact of the 3-4-5 triangle. 9 (3^2) plus 16 (4^2) DOES equal 25 (5^2)

    Thumb up 0 Thumb down 0

  11. Maths have many conditions. it should follow all those rules or not we simple get false answers and some times we may get controversial answers means if we multiply axa = square of a
    and square root of a = +a or -a but +a not equal to – a
    or if u multiply any number with zero it remains zero then
    0x1= 0x2=0x3 and so on = 0 if u cancel the zero 1=2=3= and so on then maths fails
    1 = 1 square = 1 cube =….
    a to the power of x = a to the power of y
    so 1=2=3=4=….. is it correct???

    so when ever we solve problem we must mention the limitations first
    2×3+1 = 7
    2×3+1 = 8
    both answers correct but the way of calculation procedure is not same
    if u press ur calculator 1 / 3 = u get 0.33333333 and u multiply the answer with 3 u get 0.999999 that means ? it have limitation in digits

    we cant calculate the value of pi exactly

    so that there is some tolerance is must for maths

    Thumb up 0 Thumb down 1