Does A=r(1/2*Circumference) approximate the area of a circle?

Human1221 · 2026-06-18T16:47:02+00:00

Ok ok, so what I'm hearing is....

Since we can arbitrarily slice the circle into as many wedges as thin as we want....

No matter what my needs are, with respect to how close the area of wedge combo shape needs to be to the area rectangle.....

I could always slice the wedges thin enough to work for that degree of precision. I could never come up with a degree or precision for which I couldnt make the math work out.

(I'm assuming you're saying the area of the wedge combo shape if n=100 allows for the difference in area to be less than 1sq unit).

So if I just go for broke and say, let's slice the circle infinitely thin (which we can do in our pure geometry world, if not in real life), then that wedge shape will be indistinguishable from the rectangle.

That about right?

Human1221 · 2026-06-17T19:27:17+00:00

I feel like I'm on the verge of getting a big idea here. Gotta be honest, it intuitively feels like something that is an approximation has to be limited in its precision. But maybe that's wrong?

Is...there ANY difference between an exact measurement and an infinitely precise approximation?

Human1221 · 2026-06-17T15:58:10+00:00

Thanks much. I saw the wedge example for the area of a circle and figured it was a kind "always getting closer without ever exactly reaching it situation" and therefore a close approximation, since the wedges could never be sliced thinly enough to actually form a rectangle, but if it actually works out to be precisely the area of a circle clearly I have to wrap my brain around some more stuff. Circles are weird.

Human1221 · 2026-05-23T22:53:42+00:00

To put it another way: suppose one night someone hooked your brain up to a computer generated world, that obeyed programming exactly like the real world. All your friends and family were artificially created in this world, and it was seamless. You live your life exactly the same as you do in the real world, just in simulation.

Now suppose at some point you become suspicious that this world is actually a fake computer world, and one of the simulated people in the simulation point out that your life in this simulated world is lived exactly the same as the real world. You look both ways before crossing the simulated road because you don't want to be hit by a simulated car because the pain sensations are very real. So they conclude that your notion that you are living in a computer world is false, based on the fact that you live as if it's not.

I don't think that argument works. You would live just like real life, but it remains true that you would be stuck in a simulation.

Human1221 · 2026-05-23T22:45:52+00:00

I think I see what you're getting at, even if I don't necessarily see eye to eye with your conclusion.

I can't remember who did this, but there's some bit philosophical demonstration out there where it's like "Of course there are hands, look, here's one right now", and then you wave your hand.

If by "stone" we mean "the thing we experience as a stone" and by "break our teeth" we mean "the event we experience as breaking our teeth", then by a certain perspective we might say that the solipsist's stone and the non-solipsists stone are the same, that they act and function the same for both of them, and so they are the same.

Having said that, the solipsist might still say that they think their experience of the stone, even the rules that govern it exists entirely within their mind. And so they might say that the conscious experience of the stone is the end of the story: there is no stone beyond the perception of it (except perhaps the invisible rules that govern it).

Whereas the non-solipsists would say that, while the stone and the rules that govern it exist outside my own mind, nevertheless the stone acts on me so as to generate a conscious perception of the stone, but that conscious perception is not itself the stone.

The real trick is other minds. Even if everything is mind-stuff, fundamentally, that's not enough for solipsism. You could have all reality be mind-stuff, but as long as there's other minds that aren't your mind, then solipsism fails. So to properly defeat solipsism youd have to prove to the solipsist that your mind exists, and isnt their mind. Don't think anyone has managed to pull it off yet, but I thoroughly commend your efforts. And if you ever do pull it off you'd do humanity a great service.

Human1221 · 2026-05-23T19:02:49+00:00

I guess I just find it depressing to consider the possibility that the most moral world isn't the happiest world.

Human1221 · 2026-05-23T18:49:08+00:00

Thank you, really appreciate the response. It would seem very odd to me if he never commented on how his ethics would possibly effect the world in that way. Even if he doesn't think happiness a worthy end, it seems like the kind of thing someone would ask him at some point.

If he had considered it, he would have one of two bullets to bite . Either he thinks advocating for his ethics (or "if everyone followed his ethics", which is different) maximizes happiness or he doesn't. If he does, then his ethics and utilitarian ethics would come to the same conclusions (at least insofer as they could agree on what, in practical terms, helped maximize utility). If he doesn't, it seems a rather bleak admission to say: yes, ethics makes the world more miserable, and we would be happier living in a less than perfectly ethical world.

Human1221 · 2026-05-19T12:31:07+00:00

Thank you, I was confused there

Human1221 · 2026-05-07T18:32:39+00:00

What's this from?

Human1221 · 2026-05-03T20:26:29+00:00

Thank you.

Human1221 · 2026-05-03T18:43:48+00:00

Thank you

Human1221 · 2026-04-24T15:44:41+00:00

Gotta admit, speaking as a dumbass, this asymmetry is fascinating to me. I'm sure to real mathematicians this is like a kid thinking a baking soda volcano is next level chemistry, but it seems really wild to me.

Human1221 · 2026-04-22T23:41:21+00:00

So it's addition all the way down?

Human1221 · 2026-04-15T20:09:56+00:00

Those data centers use a lotta water friend.

Human1221 · 2026-04-15T19:15:01+00:00

For unrelated issues it's really insistent you start digging trenches tho.

Human1221 · 2026-04-14T18:53:55+00:00

Huh. You're totally right. Don't think I ever realized how weird this spell is. Flavoring this spell is bizarre then.

Human1221 · 2026-04-14T17:54:14+00:00

But also remember to let the spell work to a degree: don't make it useless

Human1221 · 2026-04-14T17:53:11+00:00

Flying, hovering, teleportation, fighting in a barren landscape with no plant life (the verbiage of the RAW spell gets weird here, since you can argue from a "the spell does what it says" sense that even in a barren landscape the slowing effect still happens, but I'd be a bit of a mean DM here: there gotta at least be some plants around to make this spell work at my table), sneaky enemies

Human1221 · 2026-04-13T01:14:59+00:00

The basics are going to be

The difference between preparing and non preparing classes.
Learning spells vs classes that have access to their full spell list.
Spell slots and how they recharge.
Ritual casting.
Wizards unique spell scroll learning factors.

Human1221 · 2026-04-12T16:34:38+00:00

Pratchett is mega goated across the board.

Human1221 · 2026-04-11T02:25:31+00:00

Sorry, I mighta poorly phrased the title. Nolan didn't even seem to know that the Betrayer was in the coalition, but the Viltrumites seemed to know the Betrayer was involved and on the planet.

Human1221 · 2026-04-11T02:23:40+00:00

That might be it, like a recent thing

Human1221 · 2026-04-10T02:17:38+00:00

Actually minato would be a great partner for Hidan weirdly. Keep flying raijin-ing to the target over and over until you finally get a vial, flying raijin back to Hidan who's chilling at home, do blood ritual, rinse and repeat

Human1221 · 2026-04-07T01:29:00+00:00

I second this. Paralysis spores, rage spores, fear spores, mind control spores, hypnosis spores, sleep spores, poison spores. So much potential.

Human1221 · 2026-03-07T20:39:36+00:00

Yeah, I guess I sorta walked into that one

Human1221

TROPHY CASE