@UnderMathUate Here's a calculus problem you may enjoy. What are the dimensions of the (right circular) cone of minimum volume which enclose a sphere of unit radius? Like this:
I was going to suggest it a while ago, when xander was fishing for suitable exam questions. But given the results of that exam, it probably would have stumped most of his students...
@TedShifrin Lol. Well, in that case, I think I did learn at least a few things over the break. Plus, I don't feel like I'll be rusty jumping back into things tomorrow.
Yeah, I would never have dared give that on an exam to anything but my calculus theory students, and even for them it would have been too hard. But I did assign it for homework standardly for them.
@PM2Ring I might think about that some time. We had so many problems of that nature during my calc 3 course, so after a while, I started feeling kind of "meh".
One of my colleagues at UGA actually taught his calc 1 class partial derivatives and Lagrange multipliers (without understanding the proof with the gradient, of course). In some sense, he's right that that makes things much easier on most students.
We did one extra credit problem involving separation of variables in my calc (1 or 2?) course because it was honors. We never talked about differential equations again after that, so I don't really remember the process now, lol.
Not super related to what you said, but I just remembered that.
I played with this stuff about 15 years ago, but I recently decided to do that fractal in SVG. It took me a little while to remember how to do the small circles that are tangential to the triangles edges. :)
i deal with a lot of this stuff because my wife comes from a family where every vegetable is overcooked. holidays were torture. thankfully the coronavirus limited our obligations.
I hated brussels sprouts as a kid because my mom overcooked them (which is surprising, because my parents became pretty good cooks). I discovered when I became a cook how fabulous they are cooked properly (many options).
i had a friend in law school who insisted that i'd change my tune about brussels sprouts after i'd had her brussels sprouts. it may be possible to cook them so that they are edible but i have yet to see it.
Even the low sodium soups are too much but taste blah. Funny how I can make soup from scratch and use very little salt in a huge pot and it's totally tasty.
When my dad was dying, his body retained too much water and he could have literally no salt. For several months, I cooked with no salt and only pepper, garlic, and lots of herbs and spices. Oh yeah, and lemon.
One of my grandmothers used to put so much pepper & salt on her food that one of my cousins commented that it looked like it'd been snowing on her plate. :)
unless you're ted's dad, who did not need some salt.
that's something to consider if you get married. if you don't come from a background where it's appropriate to use a salt shaker on food after it has been cooked, being around someone who thinks that is normal will drive you crazy.
she thinks it's a courtesy. "everyone can choose how much salt to add." just cook it right. salt added during cooking is very different from stuff you just shovel onto the final product.
I suspect there's a strong correlation between boiling the life out of vegetables and auto-condimenting (the practice of adding salt & pepper to everything before you even taste it).
It's only a copyright violation if you copy a whole chapter from a book, not paragraphs. He's an idiot.
That said, I don't appreciate it when people post my exercises from my books on here and complete solutions get posted, but that has nothing to do with copyright.
But you actually know something about copyright law, I presume.
completely bogus, and by the way there are people who do this for a living. i wouldn't wade into some discussion of theoretical physics without any background. but when legal issues are involved...
I once had a xerox of Hicks's little differential geometry book, but that didn't rate keeping when I retired.
But I don't know why obnoxious, pompous ma***s has such strong feelings on this particular topic.
Why doesn't he go after all the Russian websites that upload my book and others in pdf form with zero permission ... That's totally illegal, but the publishers can't keep up with policing it.
my wife was given complete garbage advice during grad school about whether it was acceptable to employ a mathematical model created by another person for purposes of evaluating it.
the non-geographical nature of the internet makes certain kinds of enforcement effectively impossible.
There was a bit of a stir a few years ago on Physics.SE when it was discovered that someone was collecting material from there and printing it in book form. They gave proper attribution, so they weren't breaking the license conditions, but it did upset a few people that he was making money from the answers that they submitted for free.
someone introduced some set of equations and things for purposes of modeling and testing some predictions. wife wanted to see if the reported results were robust and not affected by tiny perturbations. got a VERY angry email from the author telling her not to do that and hinting at unspecified consequences. moronic, baseless, borderline harassment. her department echoed these stupid concerns.
I think I helped someone on here years ago and was asked if I wanted credit in a published article. I said it was fine if he wanted to reference it like any other source. "MSE post 5/27/11" :P
for purposes of professional ethics yes. for legal liability, in the case i am talking about, no. but this stupid person was threatening my wife with a lawsuit, not professional scolding.
there's a joke about the lawyer who says "i'm a great attorney. i've written five wills, and every single one of them has been upheld by the supreme court." the joke is that if your wills are being contested to the point that they go to the supreme court it kind of doesn't matter if you're right or not.
Surely if someone publishes a model it's desirable that others verify that the model behaves as advertised... unless your model is actually a pile of unsubstantiated rubbish. ;)
@PM2, it's your "unless" that I was suspecting must be the case. But that's all part of academic discourse. It's also the reason that "social science" is anything but science.
Ted, I'm not quite sure what's going on in your avatar image, but I think it's a rotated cube. Anyway, I did a 3D interactive version. You can interact with it on a mobile or desktop browser.
I'm still impressed that a Web browser can do those 3D calculations so quickly. Generating the shape data is done on the server, but all the stuff involved in panning & rotating is done by JavaScript code on the client.
