Sum of arctan three ways
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- čas přidán 27. 12. 2022
- Sum of arctan three ways. I calculate arctan 1 + arctan 2 + arctan 3 in three ways, using complex numbers, areas of triangles, and slopes of lines. Enjoy this beautiful algebra and geometry extravaganza that will lead you through the world of tan^-1 and pi
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Another cool general result based on this is that if abc=a+b+c, then
atan(1/a)+atan(1/b)+atan(1/c)=π/2
All them very elegant ✨️
I sincerely hope we get to see more of you Dr Peyam :)
Hi Dr. Peyam!
I thought the complex method would be my favorite until I saw the slope arguments, and now I can't decide between any of them. They're all so good!
It is my favorite visual proofs.
Wow this channel has really grown over the years. Congrats Dr Peyam!
Amazing how maths are conected in many ways
Amazing sir 💫 really fantastic one ✨
@Dr Peyam sir i have doubt in one question can you help me please
Great Dr
Nice miniature! The methods in my order of preference: 1, 2, 3. I like very much the interplay between geometry and complex numbers illustrated by method 1. And I like the geometric setup of method 2 better than that of method 3 (which I find more complicated).
Happy New Year 2023 Doc !! 🇦🇺🇺🇲
You tooooo
You should write your own math book man. You can completely change the way people see math
Thanks so much!!
I once saw the second (geometric) method in a CZcams video and liked it very much, I guess I am a fan of geomtric methods. By the way, why are you talking as if there is someone sleeping?
I didn’t want to disturb my math office neighbors 😅
@@drpeyam you are very very kind and polite. Really appreciate that
@@drpeyam sir i have doubt in other question can you please help me this out.
Hi Dr Peyam, could you make a video about finding a function whose product derivative is the function itself?
Hello sir, could you made a video watson's triple integral..
good.
I think also there is another condtion (ab + ac + bc > 1) otherwise the sum will be 0 (2pi)
Could use arctan addition formula as well but have to be careful about multiples of pi but we have pi/4
Excuse me Dr. Peyam, can you make a video about how to know the order and the degree of differential equations like this for example :
e^(y``) - y=x²
Of course, here the order should be 2nd order, but what about the degree?
Bcuz I found some say that it's undefined as long as y is an argument of the logarithmic function (when we put this equation on the linear form)✨
And other ppl say the degree is 1 bcuz they focus only on the derivatives if they're arguments or not in other functions, but don't care about y itself.
So can you please clarify this concept to make it clearer 🙏✨
That’s too specific of a question for a video
How can I get a copy of the thumbnail image? 💪
Hey Dr peyam can you upload a video about exponential integral , sine integral, cosine integral from beginning
I think I did that one
most overpowered trick: proof by calculator
0:27 -10 sure is real! That got me so hard
a, b, c needs some conditions, not only a+b+c=abc
where've you been dr peyam?!!? i miss u ;-;
I’m alive, I just have tons of work right now 😭😭
The first one and yes.
Atan(1)+atan(2)=atan((1+2)/(1-1*2)=atan(-3)=pi-atan(3)
somebody tell me how to solve this problem please🙏 especially part(A)，I have no idea
Let f : (-∞, ∞)--> (-∞, ∞) be a differentiable function such that f has a local minimum value f(−1) = -1, and the graph of y = f(x) contains an inflection point (0, 0), with a slant asymptote y = x + 1.
(A)Prove that such a function ƒ exists by constructing a possible function.
(B)Prove that there exists some a < 0 such that f'(a) = 1.
(C)Show that there exists some b> 0 such that f'(b) > 1.
How do you pronounce "Machin" in "Machine-like formula"?
Hi. I have a big challenge for you
what is the minimum distance between two points belonging to the same 3d surface f(x.y)
Too general
I like your videos
Do it pls
If f(x)=x-(1-x²)½ then find out rang of function .please slow sir
I found you from black pen red pen)
bro has been milking maths for years and it's fucking impressive.
Awww thank you 😊
@@drpeyam Adding to my original comment what I meant was it's impressive how you have been covering relatively hard things for years and they are all very relevant. Personally I always learn something that makes my general approach to mathematics better. One would have thought you would run out of equations.