Surprising rope around the Earth | Will a mouse fit under the rope? | Maths Vs Intuition

This video comes up with a very surprising and interesting result at the end and casts light on how Maths can sometimes shock and amuse us with its counter-intuitive results and concepts. It does so with the help of a question which goes like this :

You tie the Earth tightly along its equator with the help of a 40075 kilometre long rope as the circumference of the equator of the earth is 40075 kilometres. You now lengthen the rope by add 6 feet. Then you position this lose rope around the equator in a way that it is spaced uniformly across the equator. Now will a mouse fit under the rope and the Equator?

This question basically gives two concentric circles (smaller and slightely bigger circles) and asks to find the distance between the radius of the equator and radius of the circle formed upon adding 6' to the rope and spacing it uniformly across the equator. This video gives two methods to solve the problem. While it solves it by the Traditional Method to let everyone see how this happens, it also provides a very helpful tool called, "Considering Extreme Cases." This concept of " Considering Extreme Cases " is a very elegant method to solve Geometric or other Maths Problems.

Imagine tying a rope tightly around the earth along the equator, like this. You would need  40,075 km long rope to do it, the circumference of the Equator being 40,075 km. You now lengthen the rope by  6' that is add 6' which is only nearly a human length, to the 40,075 km long rope. By doing this, you lengthen it by only 0.0000045 %. Then you position this loose rope around the equator in such a way that it is uniformly spaced off the globe, like this. Now the question is, will a mouse fit under the rope?

Anyone with the knowledge of circle, radius, diameter, circumference of a circle, and little common sense should be able to solve this problem.

[salonishikha]

Whoaaaa.. Where do you get such ideas from, Mew Maths! ❤️❤️❤️

[abysmalskies]

Mind boggling Fact! Scales doesn't matter! It must be facts like these that might be giving rise to some loop which might be giving rise to imperceptible concepts like space-time continuum and expanding universe !

[mindkinds]

Made after diligent research, this video is a must watch for everyone.

[yapsiauwsoengie]

x = additional circumference
Simplified as:
2πr₁+x=2πr₂
2πr₂-2πr₁=x
2π(r₂-r₁)=x
r₂-r₁=x/(2π)

[HaiderAli]

Hi
Can you tell me what software you use for animation?