วีดีโอ

Excellent video. I like it. I have developed a new process to do waveforms like Fourier Transform. For example with this theory we can create Wavelet Transform and Uncertainty Principle graph... th-cam.com/video/p0Zc9onKQ0Q/w-d-xo.htmlsi=7xOPEEFt22GgXL8s

A Question: can we find triangular or square shape waves in nature ?

love it!!

Such an opportunity lost - remove the background music, please!

Thanks for this valuable insight!!!

great explanation , please get rid of the background music :-D

And words of gratitude to 3b1b, which first showed this way of interpreting the Fourier transform.

I hope I'm well known 😅

Most annoying background music ever

10:35 I do not understand it please,please

Nice work

Can't believe you don't have over 1000 subs... hope I can help.

intuitively speaking i wouldve thought it diverges due to the harmonic series doing so, didnt immediately see it as a product instead

very helpful video thanks! one thing that's hard for me to understand is at 5:48 when you're describing a chord, I'm not clear on how the 4:5:6 ratio relates to the frequencies 554, 698, 831?

HELLLLLLLOOOOO. Can I ask you how or which app did you use to apply Fourier transform and obtain those frequency domain graphs? I NEED IT FOR A MATH PROJECT. PLEASE HELP ME

domain ???

Great video. Thanks for making it! My only criticism is that the background music was a bit too loud (and stylistically perhaps not everyone's cup of tea)

Consequently, not consequentially.

Beautiful video. Thanks

Hi Peter that was an excellent video. I had trouble in understanding translating the time waveform about the origin, is it polar coordinate transformation of the sine wave ? I didn't understand the part where you mentioned about the degree of freedom to change frequency about the origin. Can you please clear that by siting any reference ?

Thank you!

I've been trying a whole lot to create a Python random music generator for far too long with still no progress.

amazing

The volume problem can be much simpler than that. To find the height of the cross sectional area, take (1/2a)^2 + h^2 = a^2. You have 1/4a^2 * h^2 = a^2. Subtract 1/4a^2 from both sides, then you have h^2 = 3/4a^2. Taking the square root, you have sqrt(3)/2a. Multiply 1/2(sqrt(3)/2a * a) and you get sqrt(3)/4a^2. Now you're integrating from 0 to h(height of tetrahedron), with the cross sectional area so a =0 and a = h. To find the height of the tetrahedron, draw a line connecting the left corner tetrahedron to the centroid of the base and draw another line connecting the centroid to the tip of the tetrahedron. Project that onto an a equilateral triangle with the side length of a. You should have a line bisecting the left corner of the triangle, which is x and has a 30 degree angle from the base . So using SOHCAHTOA, 1/2a/x = cos(30), x being the hypotenuse and a being the adjacent side. (1/2a)/x = sqrt(3)/2. a = xsqrt(3)/2. So x = a/sqrt(3)/2, which x = 2/sqrt(3)1/2a. x = 1/sqrt(3)a, which is sqrt(3)/3a. To find the height of the right triangle, it is h^2 + (sqrt(3)/3a)^2= a^2. So h^2 + 3/9 = a^2. H^2 = 6/9a^2, which means h= sqrt(6)/3a. So plugging that back into the bounds we have a = h, h being sqrt(6)/3a. Solving for a, we get sqrt(6)/3. So now we have the integral of sqrt(3)/4a^2 from 0 to sqrt(6)/3. Evaluating the integral we get sqrt(3)/4(a^3/3) * sqrt(6)/3 - 0. This simplifies to sqrt(18)/36(a^3). This further simplifies to 3sqrt(2)/36 (a^3). Factoring 3 out, we get sqrt(2)/12(a^3). That is our final volume.

I enjoyed the creativity in this video and learned a few things, although I share the view of others that the piano soundtrack detracts from the experience. (Thanks nevertheless)

4:28 Why is 1/cos(Pi/3)=1.99. In my calculation this is exact 2.

Reminds me of functions like fx,y)=sin(cosh(x^2+y^2).If you plot it,it's like a normal riple in the center but further out (at a finite radius) the "frequency" becomes infinite.

This is a great video, we were just given these laws in class and I didn't understand why they worked until now.

This is a really awesome video! Just one remark - in LaTeX, use \cos, \sin, etc. for trig functions, it makes them be non-italic and better formatted.

Majro seventh :)

Eye of illuminati 😁😁

What a perfect video! I wish that all of my classes on any subject would be like this, well explained and treating everything as non-trivial, thank you so much for your work Peter!

That was awesome, i knew about the fourier transform but that draw you made by wrapping the wave in a circle around the origin just shined a light in my brain about the transform i never had thought before, now the formula actually makes clear sense to me, very nice very nice thank you very much!

i love how you named it kyle

I love the formatting on these videos! It's super relaxing and really fluid. I can't wait to see what else you make!

I read this as circumcised media

Thanks!

Nice video!

How clever putting a loud background music while showcasing harmonious/dissonant chords! Very smart, thanks!

you have the issue of computational limitations, the amount of accuracy you can get is only proportional to the number of times itterated, and the accuracy of pi. all together a near infinitly small change in pi could result in the result being way off (because that change is compounded every itteration). there is no easy way around it, all of our computers will try to store the rusult and pi in a finite space each decimal place takes up space, and because we don't know if the size of the circle could be a non rational number we can't say for certain what that constant is. much like pi you can approximate it, but it also relies on an approximation of pi. unless you want to find every digit of pi by hand, then find every digit of this circle by hand, you can only really guess. and a guess on a guess couldn't be very accurate. (nit picking) that of course is to find a perfect solution. if you want an approximation do as the engineer do, look at it, measure it, call it 8.71. much like the engineer version of pi: 3.14, it is rounded to be simple and easy to use and be good enough for the job. for pretty much any measurement going over 4 decimal places is way too far, specially because with engineering there is tolerences and they normally remove material so if it is close youre changing it anyway might as well round it. sounds like im side stepping the problem, i most certainly am, it is a problem i have no need to contribute to, partily because i am not qualified in math to, and because 8.71 is good enough for me.

in the description you say finding the area of a tetrahedron when you mean volume.

You deserve far more subscribers, you're doing a great job, keep going!

A pleasant and musical video ❤️

The pacing for this video is really unnecessarily padded. You don’t need to show us a table of contents before every single section. And we know what a tetrahedron is, so there’s no need to explain that so slowly. Cut to the chase!

Similar issue with fractals, infinite perimeter, enclosed within a finite circle, infinite sides in a circle has the same issue.

🙏 Sir , Please Make a video on How Fourier Transform is the another case of Laplace Transform ?

very berry underrated

I like it so much

Circumcised mania

Great video, very informative.