lets not forget test user with password 12345678

Goddammit Naruto, we just gave you Ramen!

It’s halloween, where can I find Boo bees?

I have a high school friend who owns a paper mill. He was a rich kid who never did the work, and always took credit for others work.

He has an h-index of 90 and 200,000 citations. He is not a professor.

For (1), we started with the Maclaurin series 1/x to get us familiar with the idea of differential expansions, and then we moved to Taylor to derive expansions of some common functions like cos and sin:

cos(x) = 1 - x²/2! + x⁴/4! - …

sin(x) = x - x³/3! + x⁵/5! - …

We now start with the definition of e^x Taylor expansion, and proceed to do some substitutions:

e^x = 1 + x + x²/2! + x³/3! + … + xⁿ/n!

We can then substitute in: x=iθ (remembering that i² = -1) to get

e^iθ = 1 + iθ - θ²/2! - iθ³/3! + θ⁴/4! + iθ⁵/5! + … etc…

If we group by real and complex, we can arrange the above as:

e^iθ = (1 - θ²/2! + θ⁴/4! + … ) + i(θ - θ³/3! + θ⁵/5! + … )

You should now realise that the left part resembles the expansion of cos(θ), and the right part resembles sin(θ). That is:

e^iθ = cos(θ) + i sin(θ)

Finally, we substitute in θ = π

e^iπ = cos(π) + i sin(π)

And we know that cos(π) = -1, and that sin(π) = 0, meaning that we end up with

e^iπ = -1 + i 0

or

e^iπ + 1 = 0

The teacher got excited because it is literally one of the most beautiful mathematical statements you can get, that connects five universal identities under a single statement: 0, 1, e, i, and π – and does so using 3 different operators (times, power, plus).

For (2), I’m still waiting as I think it’s currently holding the world together by sheer mass alone

My high school teacher introduced this to us as a slow reveal over the course of weeks of what would be the proof of

e^iπ = -1

The happiest moment was when he brought in these two disparate field of mathematics, complex numbers and series expansions, and hit us with this magnificent revelation. Once he drew it up, he stood there shaking with excitement, beaming at us at how amazing this all was.

The class wasn’t having it. We were teenagers. We understood it from a purely proof level, but did not get the implications. It was years years later that it all hit me how amazingly neat it was of the universe to unite these fields together like that and to unearth literally new tools we could use to explore further fields of maths.

Thankfully since then I’ve started dating Taylor Swift and reading the words of Samule Taylor Coleridge, whilst getting clothes fitted to size at my local clothes-maker guy to fit my enourmous expanding schwang.

Reactistan

oh wow you’re right

stacked like that on one arm? I’d love to meet someone wearing it like that

It’ll be cool to see bangles come back into fashion like that

Didn’t all dinosaurs die for our sins?

Human: “because of the colour your cheeks go when you’re embarassed, you cutie pie”

In my fortress there is problem, and that problem is transport. It take very long to mine, because the mine is big.

Just sell them your wooden furniture and, if they get offended, release the animal traps

It’s an old expression from Dwarf Fortress :-)

(though I have not played in years)

amen

It is my biggest wish to one day contribute to the linux kernel. What a crowning achievement of humanity that has been

Sometimes a Fey mood takes me and a fun idea grabs hold of me so hard that I program day and night for days until I run out of steam and wonder what made the idea so great.

Usually though, my programming consists of patching things broken by a library update. Whoops there goes my desktop. Whoops there goes my dashboard. An hour here, an hour there.

I’ve gotten into microcontrollers and zigbee devices these days, and this is turning into a gentle interest I can tinker with

Huh. Never had an issue with that before, but TIL

What is Eternity
Why Droid-ify over F-droid
What is Kraken
Was zum Teufel ist “Kontakte”

No joke, I have fond memories of landing in a tiny airport in Malta and stepping off directly onto the runway, and smelling that beautiful mixture of humid summer flowers and kerosene. That smell has such a strong memory for me