I honestly aspire to be as happy as you are doing maths

Thank you, that is a lot of fun, as ever. Possible inaccuracy: The power series of the exponential begins at n = 0 I believe, in which case a -1 term would be missing, which, however, does not affect the final result (since the real part is discarded).

@drpeyam

Жыл бұрын

Yeah the original sum was meant to be from n = 0

Nothing more satisfying than expressing a infinite sum in terms of transcendental functions!

Dr Peyam, thank you very much!

سال نو مبارک دکتر پیام. برایتان سالی سرشار از زیبایی و سلامت و برکت آرزومندم

bien hecho dr peyam saludos de Perú.

@drpeyam

Жыл бұрын

Gracias!!

When you make something complex and surprisely it become more easy 😁🤭

o_o;;; this is such a thrill. Seeing this performed by someone else. Back in college... i used to tinker with the Flint Hills series. bizarre series where integers go into Trig functions, just like this. i wonder if you could perhaps give it some exploration. But.... my suggestion, try looking at it in terms of the group symmetries involved. These complex methods i've seen you use... really opened my eyes again! It's very empowering. I want to dive back in and try a few things.

Hi Dr. Peyam! Very cool!

A nice one!

i wanna b as happy as u while doin maths :)

Similiar things appear when solving y^(n) - y = 0

I'm a big fan of your videos. I just wanted to point out a small mistake. The series actually starts at n=0, so the sum of x^n/n! is equal to e^x-1. This doesn't affect the result for sin, as it corresponds to the imaginary part, but for cosine it does make a difference.

@drpeyam

Жыл бұрын

Thx

0:26 Das ist schön!

No way! So cool 😎

Thank u doctor and thank you for " uwylar identity "

Can someone help me understand. I thought e^(iN) = cos(N) + isin(N)….so how come at the beginning he replaced sin(N) with e^iN without handling the cosine ?

@drpeyam

Жыл бұрын

Correct, because you can compare imaginary parts

I've a christmas problem for you, I've a christmas tree (a cone height h and base radius r) and I want to decorate it with a strip of lights, how long it needs to be to do n complete laps around the tree while going down ending in the bottom? I think is a curious problem, I dont know if its very difficult or messy but looks fun. Anyway happy christmas!!

@drpeyam

Жыл бұрын

That does sound interesting! It would have to wait til next Xmas though hahaha

EIN Dr. Peyam pro Tag würde mein Leben reicher machen! Ja, neee, bin zwar ein Mann, aber trotzdem ... Liebe deine Videos und deinen Humor 🥰

@drpeyam

Жыл бұрын

Awwwwww

The index of sum is 0 no 1. The result is correct. Thanks for yours videos.

@orenfivel6247

Жыл бұрын

0:50 not precisely. result is correct since sin(0)/0!=0/1=0

@sebmata135

Жыл бұрын

sin(0) = 0 so I fail to see how it matters

@wulli_

Жыл бұрын

I believe what is meant is, that the power series definition of the exponential function starts at index 0 and not 1, as opposed to the video. Coincidentally, the result is still correct, as the omitted first term corresponding to the index 0, namely ((e^i)^0)/0! = 1, does not contribute to the imaginary part of the sums value.

@drpeyam

Жыл бұрын

Thank you, and yeah it really doesn’t matter

@pietergeerkens6324

Жыл бұрын

@@drpeyam I hope you don't mind: I've been using you (as well as myself) as examples for my math tutees when they make a careless algebra error: "Algebra is hard, and finicky, to get right. Everyone makes careless errors in the algebra, at least occasionally. I make them (in high school, like the wake of a cruise ship I made them); and even Dr. Peyam on KZread occasionally makes careless errors. The trick is to practice finding the errors, since they're always lurking somewhere."

0:23, you got ein eh? Insert cowboy bebop reference here.

The more languages you know, the more words you can find in your equations.

Hi I think the sum will start from N = 0 not 1 ?

@drpeyam

Жыл бұрын

Yes but doesn’t matter

how'd you write sin(N) as e^iN ?

@jadewolf3416

Жыл бұрын

Agreed. I thought writing sin(N) as complex definition is (e^(iN)-e^(-iN))/2i? Or maybe there are some cancellations that were omitted?

@fedebic5443

Жыл бұрын

He didn't, if you watch the entire video you can see that he is just building a "similar" problem with e^(iN) (which, like you mentioned, isn't the same as sin(N)) and at the end considers only the imaginary part of the solution, which corresponds to the solution of the original problem (because sin(N) is the imaginary part of e^(iN))

@HershO.

Жыл бұрын

you need to watch till the end to actually understand what he did. Edit : thought I'd mention that he uses the fact that Im(e^ix) = sin(x) which comes from Euler's formula

@drpeyam

Жыл бұрын

exp(in) = cos(n) + i sin(n) and then you take imaginary parts

A good question for Hanukkah

Wow

hermosa

Симпатичный ряд

@IoT_

Жыл бұрын

Ага. И решается просто.

When you said e i e i o LMAO!!!!!

pero la suma parte de n=0. Como estudiante, esos detalles cuestan puntaje en una prueba

@drpeyam

Жыл бұрын

No importa, sin(0) = 0

@respondepuh

Жыл бұрын

@@drpeyam me respondió en español!!

Wait isn’t sin(N) = (exp(iN) + exp(-iN)) / 2i

@drpeyam

Жыл бұрын

But also sin = Im exp

@orenfivel6247

Жыл бұрын

that's cos(N)

Nice german

@drpeyam

Жыл бұрын

Danke!!