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That almost makes sense, but pi radians = 180°
Right, a triangle “has 180deg,” like I said.
in which case π÷n is infinitesimally small. In other words, substituting infinity for n would be incalculable
That’s not how limits work. Substitution is not the same as taking the limit.
infinite and infinitesimal numbers are impossible to express rationally.
That’s not true at all. https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_⋯
It’s not about colloquialism or language
Having one word (or phrase) with two meanings is a property of language.
That’s exactly my point, there are two different colloquial ways of talking about angles. I am not claiming there is a mathematical inconsistency.
Colloquially, a “triangle has 180 degrees” and a “circle has 360 degrees.” Maybe that’s different in different education systems, but certainly in the US that’s how things are taught at the introductory level.
The sum of internal angles for a regular polygon with
nsides is(n-2)×pi. In the limit of n going to infinity, a regular polygon is a circle. From above it’s clear that the sum of the internal angles also goes to infinity (wheres for n=3 it’s pi radians, as expected for a triangle).There is no mystery here, I am just complaining about sloppy colloquial language that, in my opinion, doesn’t foster good geometric intuition, especially as one is learning geometry.
I don’t think we’re talking about the same thing.
If you take a circle to be the limit of a polygon as the number of sides goes to infinity, then you have infinite interior angles, with each angle approaching 180deg, as the edges become infinitely short and approach being parallel. The sum of the angles is infinite in this case.
If you reduce this to three sides instead of infinite, then you get a triangle with a sum of interior angles of 180deg which we know and love.
On the other hand, any closed shape (Euclidean, blah blah), from the inside, is 360deg basically by definition.
It’s just a different meaning of angle.
See, for example, the internal angle sum, which is unbounded: https://en.wikipedia.org/wiki/Regular_polygon
Triangle, “has 180 degrees,” subtends 360 degrees.
Circle, “has 360 degrees,” the sum of the interior angles is infinite.
(I’m not actually confused, it’s just that “a circle has 360 degrees” and “a triangle has 180 degrees” is a little annoying in that they use different definitions.)
6·2 days agoGiven that they specified “caffeinated tea” as also conferring benefit, I would guess it’s the caffeine that’s the active substance here.
2·3 days agoWell f2k me, T1L, t4s!
SEA vs. NE, it said so right on the TV.
…now, why Seattle-Tacoma International Airport and an intercardinal direction are playing each other is anybody’s guess. Maybe one of the runways has a nasty NorthEasterly crosswind?
Where energy efficiency isn’t a concern (maybe a blender or a toaster) this sounds nice, but otherwise…well…lots of wasted energy.
(Of course, it all has to be balanced against the cost of manufacturing/disposing.)
Heat pumps want low temperature differences, so I’m not sure you’re going to have much luck getting a heat pump oven to 475F/~250C.
35·4 days agoOr, malicious compliance by someone with a moral compass. Best is to somehow leak documents wholesale. But if that’s not possible, I think the next best way to all but guarantee that the information gets out is to do a lousy job censoring, and let “The Internet” do the rest. It also makes the administration look even more stupid, especially in the eyes of technically minded folks.
But yeah, not the best and brightest, that’s certainly a possibility.
5·5 days agoGive turnips a shot! Make sure to add a beet so they get that almost neon purple color (ok, really “argon purple”) like you find in middle eastern restaurants.
If Gentoo can be both Chad and Schizo, Slack should definitely be in the Chad category too.
I mean, it’s Torvalds’ distro of choice iirc, which should count for something.
High frequency is generally bad for transmission line losses, so getting power from A to B is better at lower frequency — DC is a great option here.
If we switched to DC, many things would still flicker though as they would presumably use switching power supplies, but those could be relatively high frequency like you said.
Interestingly, airplanes use 400Hz, as transmission over distance doesn’t matter, and transformers can be made much smaller/lighter.
The history of the smallpox vaccine is fascinating iirc — milk maids, orphans-as-storage+transportation, really crazy stuff.
And after reading about it, one thing that’s neat is that it makes sense. You don’t need to talk about homeopathic “water memory” or whatever, and you don’t even need a solid understanding of biology — the whole thing just kinda…makes sense.
And yet, here we are…
2·6 days agoThe model certainly works for other things — municipal broadband in the USA is often very well regarded.
OP needs to stop Chase-ing up votes.
12·8 days agoThey say “everything’s bigger in Texas,” but maybe that’s just because California hasn’t whipped it out until now…
From link: