Saturday, April 14, 2007

With many cheerful facts about the square of the hypotenuse

Courtesy of Chris, here is photographic evidence of the startling discovery we made a few months ago at the Glasgow Science Centre.


The idea is a demonstration of Pythagoras's theorem that a^2 + b^2 = c^2. The area (a^2 + b^2) in this case is equal to the cross-sectional area of the two smaller tanks filled with fluid.


Then we simply rotate the apparatus and let the "hypotenuse" tank fill with fluid.


The result: the larger tank does not contain all the fluid. a^2 + b^2 > c^2. Convincing experimental disproof of Pythagoras's theorem!

I think it's great that thousands of Scottish schoolchildren are getting to witness first-hand hoary mathematical theories being uprooted by real-world experiments. That is science in action!

21 Comments:

At 10:45 PM, April 14, 2007, Blogger Scott said...

That's even better than the mural at the St. Louis Science Center that depicts Earth's atmosphere in cross section — all the way up to the height at which "gravity ceases."

 
At 8:58 AM, April 17, 2007, Blogger Jordan said...

Is it that the depths (perp. to the plane of the triangle) of the different rectangles are different? Did you figure out the reason why it was wonky?

 
At 9:40 AM, April 17, 2007, Blogger Richard Mason said...

I would assume that the tanks were not quite the same depth. Perhaps the backplane of the apparatus was not quite level, although the difference was not obvious to the naked eye.

The tanks were quite shallow, on the order of a centimeter, so a mere millimeter of error would account for the approximately 5% depth discrepancy. If the tanks were deep, it would be easier to make the demonstration work accurately, but of course then the tanks would be harder to rotate.

 
At 4:28 AM, April 29, 2007, Anonymous Anonymous said...

Did you check for spatial or topological anomalies?

It is important to measure the angles of the three sides to see if they add to 180 degrees, before complaining that a^2+b^2 is not equal to c^2.

 
At 1:49 PM, September 16, 2007, Blogger Scott said...

Perhaps those responsible for constructing the exhibit accidentally used an *hyperbolic* carpenter's plane...

 
At 6:39 PM, October 10, 2007, Anonymous jonathan said...

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.

 
At 4:27 AM, October 15, 2007, Anonymous Anonymous said...

AIUTO!!!

 
At 1:25 PM, October 16, 2007, Anonymous Anonymous said...

Since yours was a practical experiment, why dont you give us the values of a, b, c, I really want to see if you can construct a right angled triangle and invalidate pythagorus theorem with a, b and c?

More over, I dont know what the depth of each tank was. If it was a cube pythagorus theorem
doesnt say that a^3 + b^3 = c^3

--Diablo
Raleigh

 
At 1:40 AM, March 29, 2008, Anonymous Anonymous said...

The formula seems to be like:

(a^2)*l + (b^2)*l = (c^2)*l

where l is depth of a tank

So 'l' cancells out (if all tanks were equal depth) and we are left with Pythagorean theorm:
a^2 + b^2 = c^2

I do not know what is the problem if triangle is right angle and all tanks are equal depth.

-------
mabs239

 
At 12:41 AM, January 16, 2009, Blogger Aleksan said...

Give it some time it will nadir...

 
At 12:49 AM, January 16, 2009, Blogger Aleksan said...

And also, is this in 2D?
or 3D... How could water fit in
Two Dimensions!

 
At 8:32 AM, February 10, 2009, Blogger Hans said...

Falling fluids heat up,
and then (mostly) expand ...

 
At 2:39 PM, February 10, 2010, Anonymous Anonymous said...

If I were a kid, I'd call this "Most boring exhibit EVER." Now if you need me, I'll be over at the Tornado Maker.

 
At 9:22 AM, June 07, 2010, Anonymous Anonymous said...

Who ever thinks this disproves the pythagorean theorem is an idiot.

 
At 9:58 AM, June 07, 2010, Blogger Philipp said...

Its trivial: the triangle is also filled at the beginning, which it obviously shouldn't be.

 
At 8:22 PM, June 07, 2010, Blogger Warrigal said...

Anonymous-on-June-7, nobody (I hope) thinks this disproves the Pythagorean theorem; the original poster was joking.

 
At 5:33 AM, June 08, 2010, Anonymous Anonymous said...

Why is this guy wearing a heavy coat and scarf? Maybe the water is freezing. Water expands as it freezes.

 
At 11:55 AM, July 30, 2010, Anonymous Anonymous said...

In order for the liquids to return to the smaller squares when rotated back to a level hypotenuse with the smaller squares on the bottom, the builder probably added a passage for the liquid to flow between them. Extra room for liquid in that passage -> extra liquid as show when rotated.

 
At 4:58 AM, July 31, 2010, Anonymous Petr said...

Nice thing about mathematics is, that Pythagorean theorem clearly disproves corectness of this experiment :)
When you prove theorem, you discover the absolute truth. There's no such thing in human culture, in nature, in science. Interesting phenomenon

 
At 1:59 AM, February 25, 2012, Anonymous Anonymous said...

If you look closely at the first frame, you can see the darker pinkish purple of the liquid in the C^2 square. not a lot, unless the angle of the camera is hiding more. This is possibly the cause for the problems when rotated. It appears, in the second frame, that the fluid enters the C^2 square via the "funnel" angles at the corners, and if it is spun or rotated, then one side will experience quicker displacement of fluid.

 
At 3:02 AM, January 09, 2017, Anonymous Anonymous said...

Depth of all tank is not equal.So, we cannot cancel out I from formula
(a^2)*l + (b^2)*l = (c^2)*l

I agree with Diablo Raliegh

---
Sakthi

 

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