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Xaviera López ²

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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.

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Coloured Faces

Artist Christina West sculpts portraits with colourful patches eroding from them. Segments of the subject’s face are worn away or chopped off, focusing the viewer’s attention on the layered interior of the busts, rather than their exterior features.

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“If you can love the wrong one so much, just imagine how much you can love the right one.”

— Brandon Stanton, Humans of New York

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Portrait of Nusch Éluard, Pablo Picasso

Medium: oil,canvas

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I guess cats aren’t so cold after all

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Tag yourself, I’m chaotic neutral

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Woman and Birds in the Night, Joan Miro

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People use the generation names so often today without even knowing them right. Here is a chart. via @ http://www.liveinfographic.com/ BasementWeebsMom, May 23, 2018 at 04:07PM

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Mommy (Source: https://ift.tt/2Il0Fat) - (Source: https://rebrand.ly/cutedogsandcats)

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Inside - Vadim Sadovski

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Our Education System In A Nutshell