Lymeregisfossils Thursday Lunchtime On The Jurassic 🦕Coast🌊 ! The “ammonite Graveyard” -a

2016 Perseid Meteor with Green Tail (x)

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.

Camping tip

Snuggly boy and his favorite toy.

Video by Marielle Tepe

Wow

After presenting the oldest known proof of the Pythagorean Theorem from the Zhou Bi Suan Jing (Chinese math book from like 1000-600BC), Bhaskara (Hindu mathematician who presented the proof, but did not discover it) ended his explanation with “Behold”.

In other news, instead of a black square, my proofs will now end with Behold.

This is how far into the earth humans have dug so far.

Cute animals ♥