The applications of hyperbolic trig | Why do we even care about these things? 

Yo flammable maths i love your channel

haha...

MUHAMMAD AVDOL?!

YES I AM

dammit, now we gotta cancel the funeral arrangements

Damn, you need to tell us more 😂

@@helloworldfromvn It's nice to share 🙂

when was this@@alphalunamare? Are you still in college? Did you go to college for your bachelor's or master's?

I’m interested but don’t quite understand what you mean by “roll”

@@trilogeee just like how you roll a ball over the ground. Imagine you have a very large physical shape that is a perfect parabola. If you start pushing it, it will keep on rolling like how a ball or an egg does. Because the concavity of a parabola doesn't change (and is positive), you can keep rolling it indefinitely.

Similarly, a square wheel rolls smoothly on a catenary. (I made a video about that, for anyone curious: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-PfLz7haFvkk.html )

@@mostly_mental nice video! I watched it all the way through and it was very clear. If you're willing to accept constructive criticism, I'd just change the way you calculated the integral. It's not ideal to have to pause and read for yourself while watching a video. But a great nonetheless :D

@@skylardeslypere9909 Thanks. The integral wasn't the important part, so I didn't want to interrupt the flow, but I can see how that would be distracting. I'll try to avoid that going forward.

he DID?

Wrong. sin(ix) = i sinh(x). And theta = - i arcsinh(2i)

@P. BPI: You should proofread your argument for it to be complete. Regards

Although an i is missing in some places there, once replaced where missing, the reverse also works: cosh(ix)=cos(x) sinh(ix)=i sin(x)

1. is also a good example of how a function can be split into an even function and an odd function that add to each other. [The general case is f(x)=(f(x)+f(-x))/2+(f(x)-f(-x))/2]

That’s what I was trying to say

Interesting!

A get that curve between the 2 rings must have a longer path than a straight line, but if you think about a ring around the catenoid, parallel to the rings, its smaller with a catenoid. So, in full 3D, the catenoid does have less surface area.

@@kindlin Thats not right. Lets say we cut the catenoid off at the heights -a and a (it should be "centered" at height 0). Then we get an expression like A_1=C*(cosh(a)sinh(a)+a) for the surface area. If we do the same for a cylinder from height -a to height a we get A_2=D*a*cosh(a) where C,D are constants. Now cosh(a)/sinh(a)-->1 for a to infinity, so A_1 behaves asymptotically like cosh^2(a) and A_2 behaves like a*cosh(a). With that we can see that A_1/A_2 goes to infity for a to infinity. That shows that the cylinder has a smaller surface area for big a.

@@cheiron8163 You're way over complicating this. A catenoid forms between the 2 rings, easily shown and google'd, which itself is comprised of a continuously rotated hyperbolic curve. The mid point of this curve is necessarily closer to the centroid of the straight-lined ring-cylinder, and so the surface has a smaller diameter and area.

@@kindlin 1. I am not talking about the ring stuff, but about a mathematical catenoid (that goes on forever, otherwise i would not talk about limits). 2. Yes, your argument explains intuitively why the catenoid has a smaller area for small height, but it cant be applied in all cases. 3. Your argument "your proof is complicated, so it is wrong, as i found an easier answer on google" is irrational (not to be rude, but you cant just reject an argument because its "complicated"). 4. If you dont trust my proof, here is a thread in math.stackexchange about the topic: math.stackexchange.com/questions/1505835/understanding-an-example-for-minimal-surface-doesnt-imply-least-area (its more complicated, but maybe helpful) 5. If you want to verify it yourself, just take the formula for rotational surfaces and use it from height -a to a like I did. You can search up the integral of cosh^2 or maybe use the definition and factor the exponentials. Maybe you trust your own calculations more than mine :) 6. Feel free to ask questions if you have any.

sin(ix) = isinhx

@@aahaanchawla5393 I remember feeling quite proud of myself when I "discovered" this relation myself! (Hyperbolic functions were not in the school syllabus)

@@sohangchopra6478 I discovered it when I was searching for a way to find trigonometric functions of complex numbers. I watched someone do it, then forgot about it, and hen derived it myself using some algebra and euler's identity.

Not all high schools teach it I heard

Kahn academy is pretty good ngl

​@@dannyCOTW like legit or just pretty good

Just grab a high school algebra book, then study geometry and trig, then move to calculus and whatever you are interested in.

oh cool thats cosh?

what benefit is gained from making the calculations of hanging cables? Less strain on the posts?

@Hisham Malik sinh and cosh

That a lot of videos

I dont think he wants to compete with SciShow

@@readjordan2257 maybe he accidentally placed this comment here instead of at SciShow

@@danielyuan9862 but they already have at least one video on those topics. So he cant be. If he said "a new" or "another" maybe.

@@danielyuan9862 however, if zach star talked about these things and it didnt deviate from his usual style, id definitely watch. But im not sure how he could unless it is all a hodgepodge video