Just Going Round And Round In Circles

Don’t really know what I’m doing right now 🙄

[crowleysfavouritedemon]

[duckythesailor]

It's happening!! I've got my ”ruth” I now need to name it before the event... 40kg, 3 mountains, 3 days, 9 miles, 6 miles, 7 miles up... Then the same back down. Probably the hardest charity event I've ever done! https://uk.virginmoneygiving.com/justkeeponrunning ! @rnrmcharity @candlelightersyorkshire #charity #fundraising #gobigorgohome #carryingtheweightforthosewhocant #3peaks #40kg #88lbs #bestgetwalking #threepeaks #nationalthreepeaks #threepeakschallenge https://www.instagram.com/p/B0nqZOwAljWZLF2cfKyJu8Rc4C7HjsaUNuuvgI0/?igshid=13fdfe2kv06uf

[fyphysica]

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.

[duckythesailor]

Sunset at sea, jobs gotta have some perks hasn’t it.... #sunset #timelapse #sunsetatsea #lifeinablueone

[duckythesailor]

Time to bring abit of @bettys1919 back to work for a bank holiday duty treat 🤫🤭 #caketin #bettys #bettystearoom #warship #sailor #RN #lifeinablueone #dutymode (at HMNB Devonport)

[duckythesailor]

From half marathon straight to sea blowing shit up 😛☺️ #lifeinablueone #sailor #30mm #75calibre #halo #thisiswhatloveis

[duckythesailor]

Sunday- Sheffield half marathon - 13.1 miles, 22km - 982ft incline with 34 kgs, 75lb of wood, metal and steel chain. All for @candlelightersyorkshire @rnrmcharity http://uk.virginmoneygiving.com/fundraiser-display/showROFundraiserPage?userUrl=Daniel-white10&pageUrl=15 #carryingtheweightforthosewhocant #charity #sponsor #makeadifference #sailor #royalnavy #engineer #children #cancer #sponsorme #justgiving @runningworld @runningworld @runr_uk @runnersworldmag @worlderunners @runners_of_insta @sheffieldhalfmarathon @jtrunforall

[duckythesailor]

Having a great mental day and riding through the day and dealing with life problems like....

[tastefullyoffensive]

(via SilviuMajor)

[duckythesailor]

Numbers through and getting ready for the bug run next Sunday @jtrunforall raising money for obviously @rnrmcharity and also @candlelightersyorkshire I’m currently looking for a sponsor or two so if anyone knows of a company willing to sponsor a idiot point them my way ☺️☺️ https://uk.virginmoneygiving.com/fundraiser-display/showROFundraiserPage?userUrl=Daniel-white10&pageUrl=15 #sheffieldhalfmarathon #anchor #anchorsaway #34kg #75lbs #sailor #rnrmc #candlelighters #charity #fundraiser #sponsorme #carryingtheweightforthosewhocant (at Watersons News)

[photogs-lab]

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[tastefullyoffensive]

The hero we need. (via zipoffs)

[duckythesailor]

When you stop feeding her and she’s angry.... #peckish #nibbles #feedme #justwantfood #nomnomnom