@@ron-mathAnd if it's that far out in space, we can't see it either. Fortunately for all of us, we can suspend disbelief for the sake of a cool animation that helps to explain things! :D
I can't help but point this out. Doesn't the fact that you're talking about magnitudes already assumes the Pythagorean theorem?? In that case this would be a circular proof.
Can we not calculate magnitude in some non orthonormal basis where Pythagoras theorem is not valid? That's just the metric tensor right. And in orthonormal basis it gives the Pythagoras theorem.
@@luce1F I thought about it and my doubt was caused because of how quickly I think of the formula for the magnitude of a vector when it's mentioned!! That formula does use the Pythagorean theorem, but of course in this video there is no need to calculate the magnitudes based on the coordinates.
one of the edges would be at an angle relative to the coordinate axis, which would change the angle of the force vector and in turn, change the radius as we calculate the rotation around the vertical axis.
@@ytbytb-pf6jfgot it thanks. Consider an alternate problem, assume the hinge is at the right angle instead and the triangle is isosceles. Now applying the same logic give asqaure + bsquare = 0 ( as now c torque is 0), something is wrong here but idk
@@ytbytb-pf6jfI know that c force cancels with hinge normal force but what about the sides torque? Oh wait they are in the opposite direction so they cancel. The calculations would be lot more interesting if it's not isosceles
I would hesitate to call it a proof. We have made a calculation, and found that if sq(a) + sq(b) = sq(c) there will be no rotation. Now we can go in one of two directions: we can say that since the result is Pythagoras's law, we predict no rotation. Or, if we have never heard of Pythagoras, we can go do the experiment, observe no rotation and discover Pythagoras. If this demonstration is a proof, it hinges (😊) on our intuition that there will be no rotation. I don't think that is sufficiently rigorous for a mathematical proof.
It is not about intuition. It is Newton's laws at work (as mentioned in the video), which in turn are derived from and confirmed by physical observation.
I'm sorry, but the linear algebra you've used to calculate the torques is derived using the Pythagorean Theorem. This 'proof', while ingenious, is a classic example of circular reasoning.
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](http://i.ytimg.com/vi/p6j2nZKwf20/mqdefault.jpg)
![Pythagoras Would Be Proud: High School Students' New Proof of the Pythagorean Theorem [TRIGONOMETRY]](/img/tr.png)
I love the creaking sound of the frictionless rotation. ❤
If it makes noise, it’s not frictionless. If we can hear it, it’s no longer vacuum. I hesitated to add the sound effect haha.
@@ron-mathAnd if it's that far out in space, we can't see it either. Fortunately for all of us, we can suspend disbelief for the sake of a cool animation that helps to explain things! :D
@@ron-mathbut if it's in deep Space then doesn't that imply it's frictionless since there is no surface..or osnit some kind of internal friction?
Dang, that's cool! As a physics major, I appreciate this a lot!
This is exactly my reaction when I saw this proof for the first time!
same here! really nicely done :)
@@ron-mathyou didn't come up with it? Then who did?
I can't help but point this out. Doesn't the fact that you're talking about magnitudes already assumes the Pythagorean theorem?? In that case this would be a circular proof.
Hi! Can you elaborate the idea here?
Can we not calculate magnitude in some non orthonormal basis where Pythagoras theorem is not valid? That's just the metric tensor right. And in orthonormal basis it gives the Pythagoras theorem.
@@luce1F I thought about it and my doubt was caused because of how quickly I think of the formula for the magnitude of a vector when it's mentioned!! That formula does use the Pythagorean theorem, but of course in this video there is no need to calculate the magnitudes based on the coordinates.
@@ron-mathhow is the yellow surface the hypotension when it doesn't look like a right triangle. ? You cut it in half?
That was actually pretty clever.
finally, I'm ready for the geometry exam tommorrow
wouldn't the same logic be used for any triangle? not just right angle and show that asquare + bsquare = csquare? where's the flaw?
one of the edges would be at an angle relative to the coordinate axis, which would change the angle of the force vector and in turn, change the radius as we calculate the rotation around the vertical axis.
@@ytbytb-pf6jfgot it thanks. Consider an alternate problem, assume the hinge is at the right angle instead and the triangle is isosceles. Now applying the same logic give asqaure + bsquare = 0 ( as now c torque is 0), something is wrong here but idk
@@ytbytb-pf6jfI know that c force cancels with hinge normal force but what about the sides torque? Oh wait they are in the opposite direction so they cancel. The calculations would be lot more interesting if it's not isosceles
Dang it, I thought you were going to add 2 perpendicular vectors. This could have been more inTeRestiNg.
Hi. Can you be more specific like at what timestamp add what vectors?
I would hesitate to call it a proof. We have made a calculation, and found that if sq(a) + sq(b) = sq(c) there will be no rotation. Now we can go in one of two directions: we can say that since the result is Pythagoras's law, we predict no rotation. Or, if we have never heard of Pythagoras, we can go do the experiment, observe no rotation and discover Pythagoras.
If this demonstration is a proof, it hinges (😊) on our intuition that there will be no rotation. I don't think that is sufficiently rigorous for a mathematical proof.
You are right. To human in this timeline, "re-discovery" is probably more proper.
It is not about intuition. It is Newton's laws at work (as mentioned in the video), which in turn are derived from and confirmed by physical observation.
I'm sorry, but the linear algebra you've used to calculate the torques is derived using the Pythagorean Theorem.
This 'proof', while ingenious, is a classic example of circular reasoning.