Видео

Savage

Nicely done! I learned a lot from this video

Can you share video code??

Can you share video code??

Your mic is amazing 🤩

Fantastic video, simple and elegant, God Bless, Keep up the spirit, have a good time🎉

That was good ... too good explaination 😌

I would just probably integrate Bruteforce way

🔥🔥🔥💯🥂🥂

great video!

Honestly great video, I remember struggling on this problem before giving up after a few hours. About the mic quality. I think your setup is likely fine, just needs two things. One, move away from the mic by probably ~6 inches. Second, dont direct your mouth directly at the mic (this is fine with some, but probably not with yours), the main 'gust of air' coming from your mouth should pass just above the mic. This will prevent the sort of super intense sound you get with "p" or "k" sounds. Good luck and cheers!

An easier way to demonstrate why the rectangles and triangles are related is to slide them over to make parallelograms of the rectangles first / make the triangle first then slide the tip Echoing what people have said about audio quality. As for the rest of the video I really enjoyed the presentation and I really look forward to see what’ll come of it! Always happy to come across quality maths channels :)

One thing is still disturbing me, that is, wether this equation is dimensionally equivalent. Because one side is area and the other side is (arc) length.

Good stuff. I call this base 1 math. Because of exponentiation, it wouldn't reduce to Theta if the radius were any larger. (But it would be 2x) But this same principle is how calculus and a circle's area works. The curve determines its area. It's also why Heron's Formula doesn't work that well outside of Base 1. But a+b+c=a*b*c is always a triangle. No matter how you calculate it, but the most elegant nuances are found in base 1.

amazing

Amazing video, thank you!

thanks, I liked it.

Haven't watched the video, here's my solution: Let's take radius of the circle as a unit. Let's say the arc starts at angle a1 and ends at angle a2, a1<a2. The area of the D-shaped thingy between arc and a line between its ends is L=π(a2-a1)-sin(a2-a1)/2 That is the area of pizza slice minus triangle. a2-a1 is the arc length. Then A and B can be calculated as L+(area of a trapezoid). A=L+½(cosa2-cosa1)(sina2+sina1) B=L+½(sina2-sina1)(cosa2+cosa1) If we add up A and B, and distribute parentheses, we'll find out that everything simplifies to A+B=2L+cosa1sina2+cosa2sina1=2L+sin(a2-a1)

cool vid, pls fix your mic plsplsplspls

amazing video! thanks a lot! keep up the good work!

Nice problem; and very elegant solution. I approached it algebraically. With θ as you've assigned, let σ and τ be the 1st quadrant arcs above and below s respectively. Then A = ½ ( σ - sin(σ)cos(σ) ) - ½ ( τ - sin(τ)cos(τ) ) = ½ [ (σ - τ) - ( sin(τ)cos(τ) - sin(σ)cos(σ) ) ] = ½ θ - ½ ( sin(τ)cos(τ) - sin(σ)cos(σ) ). Likewise B = ½ θ - ½ ( sin(σ)cos(σ) - sin(τ)cos(τ) ). Summing then gives A + B = θ = length(s) as required. Not as elegant - but I believe also reachable by a young audience. I'll keep an eye out for your content - but won't subscribe until you get the audio fixed up.

Great👍👍👍🗿

Nice

Gotta increase sound quality. Animations are nice though.

A more straight forward approach would be to simply find each of the areas using integration and adding them. take coordinates of the points as (rcosalpha,rsinalpha) and (rcosbeta,rsinbeta) and the curve is x^2 +y^2 =r^2. Integrating and adding gives r^2 (beta-alpha) =r*arc length

Cool

this was glorious the whole way through

Un alt mod de abordare a demonstrării formulei integrării prin părți, extrem de elegant, distinct de ceea ce ătiam din școală. Foarte frumos. E o plăcere să urmărești așa ceva. Succes în continuare.

I’m not sure what audience this is intended for so take my criticism with a grain of salt. I think that the video is fantastic, however, if the intended audience is those unfamiliar with integration by parts, I think there should be some audio explaining your logic as I can imagine this might be more difficult to follow for less experienced viewers. Keep up the good work!

It is a great video, but I did not understand that (1:36) why the length of the short side of the rectangle is dx or du?

THIS VIDEO IS SO GOOOD MAAAN THXX KEEP UP THE GREAT QUALITY 🗣️🗣️

amazing work man. Keep it up.

Hey all, this is my first video of this summer and I plan on posting a bit more frequently over the next few months. Be on the lookout for those videos in the future!

nice video, congrats on showing up in the google video suggestions when you google "4d hypervolume"

جميل

Plain and simple. I never understood the "theorem" status of this. It's always been the law of Pythagoras as far as I'm concerned.

Love it

Nic

My favourite.

Cool video

Ahh yes. Pythagoras twisted squares. One oof math's many great puzzles. I like to do summation. Take a square, now make a square inside that that is 1/2 the parameter of the first square. Now make another square inside the 2nd square that is 1/2 of that. Do this to infinity and ask the question. What is the total area of the squares? What about parameter? What about the length of just one side? How about every other square, or every 3rd square, or what about the squares that fall on prime numbers? I like thinking about math like this all the time. Twisting, flipping, mixing, all to see what comes out.

there is a way i like even more is by rearranging the pieces, you can make two squares: one of side a² and the other b². since the triangle or the big square did not changed (we see it visually) then a²+b²=c²

dam nic

u could have make this video in shorts it was going viral

Met