Intuitively, this makes it seem if the coastline paradox can have a similar conclusion. That an island has an infinitely long coastline, but a finite area?
Sir, Please provide another link in description for understanding integral formulas of surface area and volume. Video was really amazing and I learned a new point of view to observe things. 🙏🙏🙏🙏🙏🙏
The assumption that 1/infinity is zero is the flaw. 1/infinity APPROACHES zero but never gets there. Therefore you never actually get the volume exact either. Conundrum solved. You’re welcome.
Calculus is based on limits. It should already be understood that 1/infinity approaches zero. Saying "1/infinity is zero" is just a shorthand way of saying that. There's a formal definition and a practical definition. I always tell calculus students to think of zero and infinity as reciprocals of each other. 1/zero is infinity, and 1/infinity is zero. Even though that's not technically true, it definitely leads to a more intuitive understanding.
What if we put the first horn inside another horn using f(x) = 2/x from 1 to infinity, then filled that larger horn with painy. Would that not paint the outside SA?
The paint would eventually reach terminal velocity and would not get faster but as the horn is infinitely long it cannot reach the end of it technically yes you could have enough paint to do it but it would be impossible for the paint to reach the end
That's the formula for the volume of a solid of revolution. When integrating solids of revolution, you are essentially adding up an infinite number of circles (or infinitely thin cylinders). The area of a circle is πr^2, so it makes sense that their sum would also contain π. When you factor the π all the way out of the integral, that's the formula you get.
Not trying to be difficult but there are a number of problems with this proof. Pi is accepted as a finite volume. Pi is neither finite nor a measurement of volume. No one will ever mathematically prove either of these claims. That strongly implies that there is something wrong. Part of the problem is that pi is indeterminate. An indeterminate number cannot be used in finite measurements, only an approximation can be used. No one has ever used the exact value of pi in a finite measurement because the exact value of pi will never be known. There's other points to dispute this, but I'm not trying to be an ass. Have a good day.
@@michael2974 Pi is not a volume it is a number. Pi is not indeterminate. Indeterminate means multiple possible value but Pi has only one value this value is fix and does not change and it can be defined exactly with a series, a limit or a formula.
@@kazedcat I didn't say pi was a volume, the video makes that claim. Indeterminate means an unknown value, not multiple values. It's easy to look it up. If pi has a fixed value, please tell me what value would be.
Absolutely loved that visual metaphor with the paint!
Intuitively, this makes it seem if the coastline paradox can have a similar conclusion. That an island has an infinitely long coastline, but a finite area?
That's interesting! You're right, it does seem that way. Like a similar situation, but everything is scaled down by one dimension.
Sir, Please provide another link in description for understanding integral formulas of surface area and volume.
Video was really amazing and I learned a new point of view to observe things.
🙏🙏🙏🙏🙏🙏
This is fascinating! I haven't heard of it before. 🙂
Very interesting and educational video. Never heard about this before
Thank you! 😃
The assumption that 1/infinity is zero is the flaw. 1/infinity APPROACHES zero but never gets there. Therefore you never actually get the volume exact either. Conundrum solved. You’re welcome.
Calculus is based on limits. It should already be understood that 1/infinity approaches zero. Saying "1/infinity is zero" is just a shorthand way of saying that. There's a formal definition and a practical definition. I always tell calculus students to think of zero and infinity as reciprocals of each other. 1/zero is infinity, and 1/infinity is zero. Even though that's not technically true, it definitely leads to a more intuitive understanding.
You are correct, 1/∞ is ε
However, I do not care because it does not get me anywhere neither in practical nor pure mathematics
What if we put the first horn inside another horn using f(x) = 2/x from 1 to infinity, then filled that larger horn with painy. Would that not paint the outside SA?
It would if you were using "mathematical" paint. But not "real" paint.
Let’s bring in our old friend the super task and knock this job out and head to lunch. :)
Wow, actually learned something, my math teacher could never-
Fun fact:although the volume is π it is impossible to fill as it would never get the the bottom
The paint would eventually reach terminal velocity and would not get faster but as the horn is infinitely long it cannot reach the end of it technically yes you could have enough paint to do it but it would be impossible for the paint to reach the end
Why is there a phi in next to the intergral at 01:23 (my friend ask me[were at the debate situation])
That's the formula for the volume of a solid of revolution. When integrating solids of revolution, you are essentially adding up an infinite number of circles (or infinitely thin cylinders). The area of a circle is πr^2, so it makes sense that their sum would also contain π. When you factor the π all the way out of the integral, that's the formula you get.
Area is in 2D, while paint on surface is 3D because paint has thickness.
Are you referring to real paint or mathematical paint? 😉
@@LearnPlaySolveif math paint is 2D, then math paint. 2D paint has no volume, so even a tiny drop of paint is good enough fir infinity area.
Nice video, but i don’t understand What we have : 2 pi […] sqrt 1+ (-1/x**2)**2. At the start for the surface.
I'm sorry, I wish I understood your question. Would you mind restating it?
But pi has infinite digits which means it's not finite by any sense of the word.
π is finite because it is bounded from above and below 4>π>3.
Just because a decimal has infinite digits, that doesn't mean the number itself is infinite.
Not trying to be difficult but there are a number of problems with this proof. Pi is accepted as a finite volume. Pi is neither finite nor a measurement of volume. No one will ever mathematically prove either of these claims. That strongly implies that there is something wrong. Part of the problem is that pi is indeterminate. An indeterminate number cannot be used in finite measurements, only an approximation can be used. No one has ever used the exact value of pi in a finite measurement because the exact value of pi will never be known. There's other points to dispute this, but I'm not trying to be an ass. Have a good day.
@@michael2974 Pi is not a volume it is a number. Pi is not indeterminate. Indeterminate means multiple possible value but Pi has only one value this value is fix and does not change and it can be defined exactly with a series, a limit or a formula.
@@kazedcat I didn't say pi was a volume, the video makes that claim. Indeterminate means an unknown value, not multiple values. It's easy to look it up. If pi has a fixed value, please tell me what value would be.