Childhood Christmas Be Like Time Of Celerbration And Presents.

This is literally exactly how our campaign is going

Turns out the knife was cursed

“I pick up the knife” is now a mini-meme among my party and obviously it just means “I did something impulsive and now it’s going to take two sessions to solve.” 

Star Trek: Deep Space Nine "Past Tense, Pt. 1"

endgame was so basic. what if when the avengers confronted thanos on his farm he was like “they said it would work. they said I would be happy” and it turned out he was just a puppet for some higher, more terrifying power. whoever it was had taken advantage of thanos’ madness and strength and used him. the film could have been about hunting down this entity and after years of searching, they find out it was the grandmaster and his brother the collector, two of the oldest beings in the universe. at this point the avengers are desperate and they can’t understand why the brothers would have done this. they need closure, they need a reason, and it turns out, after all that, the brothers were bored. they’re millions of years old and life had been getting dull so they wanted to stir the pot, mix things up a bit, so they spent thousands of years plotting an elaborate plan. they ignited the fire and watched it burn. that’s it. how would the avengers of handled that? to know that that trillions of lives were snuffed out of existence because of the tediousness of immortality? what would happen next?

MERRY CHRISTMAS

Friend: Why do you spend your time reading gay smut fanfictions?

Me:

This is the Nugget of Friendship.

It is not given lightly. Yet I give it to you.

Yes. I mean YOU.

Now shoo.

Pass on the Nugget of Friendship.

twinkle twinkle otp

you will be the death of me

always keeping me up late

reading bout your stupid dates

twinkle twinkle otp

WHY CAN’T YOU JUST LEAVE ME BE

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.

When someone tells you you’re too old for cartoons.

A school of fish following a duck