This can be done from deductive reasoning also. Each ant is travelling perpendicular to the ant that is following it so never, itself works to be further or closer to the ant that is approaching it. Thus the approaching ant is always moving closer to the ant it is approachiing at a constant speed. Thus it will close the distance in the same time and thus the distance is the same.
So in the last integral calculating the length the ants travel, theta being infinite means they end up going around the point of origin infinitely many times in like last 1% of that curve?
Yes, that's exactly right. Since the "ants" in this problem are just mathematical points, they have no size or dimension. That means they will never actually "collide" in the middle. They will circle each other an infinite number of times. However, somewhat counterintuitively, their path actually has a limit, which is equal to the side length of the square they started on.
@@LearnPlaySolve Thanks. I do keep in mind that those ants are just dimensionless points with zero size, it is just that from the the graph of their path it looks like they meet after, I dont know, like 1.5 half complete turns? Which is in contrast with the bounds of the integral, that suggests they make infinitely many complete turns, so I just wanted to be sure. P.S.: Technically, if they are moving with constant speed, than they will meet in a finite amount of time (during which they circle each other and the center infinitely many times, but that is a headache for another day :) ). P.P.S.: I really enjoyed the video, first one I saw from this channel, gonna check out more.
@@tomasstana5423 The interesting thing is that after 1.5 half-turns the ants have actually covered 99.1% of their journey. You can see that at 7:15 when the limits are plugged in that if the upper limit were 1.5 half turns = 1.5π radians = about 4.712 radians, then the definite integral would have a value of 1 - e^(-4.712) -- rather than 1 - 0 -- and that is approximately 1 - 0.009. During the last 0.9% of their journey, they do an infinite number of turns, but travel almost no distance. They do meet in a finite time, of course.
Thank you for sharing that. My goal is not to solve a problem in the shortest amount of time. My goal is to entertain and educate by demonstrating calculus concepts, using interesting and sometimes counterintuitive problems. For me, I value the process of problem solving over the end result. Thank you for watching. 😃
This can be done from deductive reasoning also. Each ant is travelling perpendicular to the ant that is following it so never, itself works to be further or closer to the ant that is approaching it. Thus the approaching ant is always moving closer to the ant it is approachiing at a constant speed. Thus it will close the distance in the same time and thus the distance is the same.
This tied more than one calculas subjects nicely and in satisfying way
You're the best. I couldn't figure out the math behind this exact situation,but now I got it. Thank you
Keep going with those fun calculus exercises! I am in love with your content, good job!
Amazing problem.
Beautiful way to learn and enjoy with calculus. Thanks
Please do more videos 🥺 I love these
Loved the explanation, pls do more
I like how things like this are presented nicely! subbed
very interesting
wow very nice videos 👍 you need more subs nice animation and voice
So in the last integral calculating the length the ants travel, theta being infinite means they end up going around the point of origin infinitely many times in like last 1% of that curve?
Yes, that's exactly right. Since the "ants" in this problem are just mathematical points, they have no size or dimension. That means they will never actually "collide" in the middle. They will circle each other an infinite number of times. However, somewhat counterintuitively, their path actually has a limit, which is equal to the side length of the square they started on.
@@LearnPlaySolve Thanks.
I do keep in mind that those ants are just dimensionless points with zero size, it is just that from the the graph of their path it looks like they meet after, I dont know, like 1.5 half complete turns? Which is in contrast with the bounds of the integral, that suggests they make infinitely many complete turns, so I just wanted to be sure.
P.S.: Technically, if they are moving with constant speed, than they will meet in a finite amount of time (during which they circle each other and the center infinitely many times, but that is a headache for another day :) ).
P.P.S.: I really enjoyed the video, first one I saw from this channel, gonna check out more.
@@tomasstana5423 The interesting thing is that after 1.5 half-turns the ants have actually covered 99.1% of their journey. You can see that at 7:15 when the limits are plugged in that if the upper limit were 1.5 half turns = 1.5π radians = about 4.712 radians, then the definite integral would have a value of 1 - e^(-4.712) -- rather than 1 - 0 -- and that is approximately 1 - 0.009. During the last 0.9% of their journey, they do an infinite number of turns, but travel almost no distance. They do meet in a finite time, of course.
Love it
Why are there few videos?
Sorry. I'm currently making more. Thank you for asking. 😊
because he is not a machine and making high quality videos takes time.
😍😍😍😍
This a can be done in one step using relative velocity concept 😂
Thank you for sharing that. My goal is not to solve a problem in the shortest amount of time. My goal is to entertain and educate by demonstrating calculus concepts, using interesting and sometimes counterintuitive problems. For me, I value the process of problem solving over the end result. Thank you for watching. 😃
How
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