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I made something

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.

PLEASE PLEASE I NEED YOUR HELP

at school, i abaolutely loved math and physics. I studied a lot at school and got straight As in every subject. But i am at university now and my Grades are so bad. I study math and physics and i really thought that i would be goot at university. I did my work throughout the Semester, and i prepared myself for the exams. I got the results today and i almost failed my exams. Now i am feeling like the biggest dumb ass on earth

So is anyone out here who could give me some tips on how to successfully study for scientific subjects at university?

Any help is appreciated

I go 2+4= 6 so 60 8+8=16 so 7+8=15 60+15= 75

Auf in die Welt der vierten Dimension ...

Der Sprung von der Fläche zur Ebene ist auch für Laien nachvollziehbar. Aber Mathematiker*innen wagen sich gerne weiter vor: Alicia Boole widmete ihr Leben der Suche nach regelmäßigen Körpern in der 4. Dimension - und sie wurde fündig, obwohl ihr als Frau zeitlebens eine universitäre Ausbildung verwehrt blieb. Auf ins Land der Polytope!

Post #116: YouTube, Arte, Mathewelten, Die vierte Dimension, 2024.