what’s a hava do?

Or they’re all chimeras, but the frog part is hemizygous (so has to express the gene) and the piggie part is X recessive heterozygous (so has another allele that can suppress the gene), and the gene controls which end of chimeric scale (frog to pig) the body tips

He was 3 days from retirement, and not a single damn thank you card

blondie: “your colleague ratted on you, said you were selling these for high margins.”

manager: “h-he said that?”

blondie: “he practically sang, and now he’s dead. We can put it all on him and call it a day, or I can tell the feds that you were the mastermind behind the whole show.”

manager: *sweats*

blue shirt: “w-we just… we just need a price. Please.”

nmtui is the best, I just wish network manager played a little better with wireguard

One short story explains the other

I was gonna ask why the reporter is wearing sunglasses indoors, but then I noticed the teeth

Is it not the 5 course dinner kicking in?

Me: “I must go now, my planet needs me.”

Them: “Don’t you live on Earth?”

Me: (already outside)

Im an anything bird - by that I mean that caffeine dictates my schedule.

If I work UK timezones, then my last coffee is at 3pm and I’m in bed by 11:59pm and up at 8ish.

If I work US timezones, then my last coffee is at 8pm and I’m in bed by 4am and up at 12:01pm

Took me a while to realise the witch didn’t have a goatee

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.

Didn’t all dinosaurs die for our sins?

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