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Conclusion: I should not consume caffeine based pain killers
Sometimes I'm "that" person. I take to statics with fond memories of vectors from my trouble causing multivariate days and my appreciated too late linear days, allong with a bystanders view of euclidean geometry. This is to say: I draw a mean triangle and think I know more than I actually do.
So when the problem is posed in such a way that it forces one to make one of two conflicting assumptions, I cant help myself.
And when I find that the solution most people will be bringing in makes both of those conflicting assumptions.... something in me can't resist.
I'm 2 pages in on a 4 page detail of why said assumptions break the problem, steadily on my way to the conclusion that the problem statement is ill posed, when I realize what I've done. Ive taken caffeine based pain killers, at night, my resting heart rate shoots up to a conservative 100 beats per minute and my hands are too shakey to write clearly.
I am forced to succumb to a different conclusion: I should not consume caffeine.
That said...I have an explanation. I just hope its correct and not a caffeine + exhaustion based misinterpretation of the problem.
I started using Synfig Studios 2 days ago and here’s what I got .
A short note on how to interpret Fourier Series animations
When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.
They are absolutely remarkable to look at. But what are the circles actually doing here?
Vector Addition
Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:
This kind of looks like a square wave but we can do better by adding another harmonic.
We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:
And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:
Source
The trajectory traced by the resultant of these vectors gives us our waveform.
And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.
Have a good one!
**More amazing Fourier series gifs can be found here.