Sometimes the best way to explain something is to demonstrate it.
December 19th, 2012 at 5:31 am
All teaching should be practical, like this!
December 19th, 2012 at 8:35 am
This is an interesting physical demonstration, but it offers no insight as to why the Pythagorean Theorem is true.
December 19th, 2012 at 8:55 am
You must be kidding.
Ignoring the fact that these are 3D cubes with volumes of water. Look at it in 2D and look at the Pythagorean Theorem. It’s a great demonstration.
December 19th, 2012 at 9:08 am
@SOB: Actually, it’s NOT a demonstration (in the scientific, formal sense). For example, the theorem could be wrong by a 1% or so, and you would not notice it from this visual. @Jim is right in the sense that there is no formally correct series of statements proving the theorem.
It is however, a very cool (and known for many years) exercise. Old math teachers (me included) used to be do the trick with sand.
December 19th, 2012 at 9:36 am
@Zorzal what criteria is needed to constitute a “scientific, formal proof” in your understanding? I’ve seen a number of mathematical proofs for the pythagorean theorem that all seem grounded in sound logical reasoning. Granted, without an explanation behind it this gif is simply a demonstration of why the pythagorean theorem works, but there are a few proofs as well.
December 19th, 2012 at 10:42 am
Maybe Zorzal would be happier calling this an “illustration.” And it’s a good one, though it could be off by 1%. As Blorgon points out, there are LOTS of formal proofs. But Jim is right: it doesn’t tell us why it works — it only shows us (very effectively) that it seems to work for this particular triangle.
I recently gave an assignment to preservice teachers with seven or so URLs for youtube videos about the Pythagorean Theorem. The discussion about which were proofs and which were demonstrations, and how we might use them with students, was really useful.
December 19th, 2012 at 12:39 pm
December 20th, 2012 at 7:32 am
I’d rather see a useful example of how and why we would use the pythagoream theorem in the real world. Let’s say you need to calculate a distance on a map e.g.
Without that useful problem to solve the pythagoream theorem is nothing but a silly game or puzzle. Granted, some students like puzzles, but most are bored to death by anything math related.
It’s better to have an actual treasure hunt, where the ones who solve the equations are the fastest to get to the treasure.
December 23rd, 2012 at 4:34 pm
I agree, note this only should proove it’s true for this triangle, not for all the rest. But I love it and will show it to my students.
December 27th, 2012 at 8:08 am
How can one know that all three of those cuboids have the same height?
December 27th, 2012 at 3:54 pm
be koz C^2=a^2+b^2
December 29th, 2012 at 6:35 am
Great presentation! Really useful for the teachers.
Chujnia na maksa. Wykop Kurwa.
December 29th, 2012 at 9:07 pm
@Goras Great=Chujnia? the teachers=Kurwa? You sabotage Google Translate ;P
December 30th, 2012 at 4:22 pm
Fajnie kurwa, ale tu jest internet i tu się komentuje po polsku 🙂
January 24th, 2013 at 8:58 am
@Jim: that’s why it says “demonstration”. Nobody pretends it’s “proof”.
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