Does you school library lend out laptops for this sort of thing? Or, can you remote into a library/lab computer for this?

I would definitely opt for a dedicated machine, running the recommended OS, no VM, as others in this thread have said. It’s one thing if it’s for a homelab, but for coursework…not what I’d be comfortable with.

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 n sides 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.)

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?

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.

Grouping SF with Oakland is also a little weird IMHO — quick googling suggests that SF muni has about 3x the ridership of BART in SF.

Sounds like we’re going to find out who the real “don’t mess with Texas” folks are vs. who are the posers.

Chuck Yeager’s Air Combat would ask for various airplane specs (“what is the service ceiling of an F-4E?,” “what is the ferry range of a MiG-15?”), and you had to flip through a booklet to find the answer.

You could copy the book, but it was fairly long so I guess the friction kept you in check.

Never tried it, but hot peppers can be added to birdseed to prevent this — birds aren’t sensitive to capsaicin, so it only affects the mammals.

Gnarly PDEs aren’t exactly the same beast as differentiating single variable polynomials.

Sounds like this was basically the plot of the first Nolan Batman.

If you really want to try some, you could use d-limonene. It’s just orange oil (like you get when you squeeze an orange peel), is edible, and is basically a kerosene-like hydrocarbon. It’s used in hand soap and works for stripping paint, and you can run multi-fuel camp stoves off of it, too!

Careful ingesting it though, as it isn’t always food grade due to extraction methods/additives. It causes kidney tumors in rats, but the mechanism is known and is not relevant to humans.

Obviously you should use an exponential search, assuming you don’t know the age of the oldest human.

Torvalds uses it too I believe, so you’re in good company (Debian for me, though my heart belongs to Slackware).

I’m not sure they’ve had bugs as severe as CVE-2023-4863 though?

VNC? You have your choice of servers, and clients are ubiquitous.

A big gotcha is that you need to be careful with encryption/security, as in classic UNIX style VNC does one thing (remote desktops). It’s easy to forward over ssh though.

You can also use VNC to share, which is not what you want; this depends on the type of server/settings. But you can definitely create a new virtual X11 session and access it remotely.

Huh, it’s not like there are any security issues with it…

San Francisco’s current trolly bus fleet are from New Flyer, a Canadian company, though they use German motors.