The only thing I will be happy about if my work will turn up as a mistake and a counterexample will be found is that I did not succeed in proving something wrong.
With these final words, I have six hours of sleep left, I should use them to get better from this annoying cold.
Besides I didn't follow the title: "This is the most difficult question I could get without using mass point geometry. Thanks in advance?" Any guesses what the OP means?
Yes, I remember that. I am uncertain what the lower left number means. I know that Asaf says it is the number of rooms attended, but others say it isn't.
no way: I've come to you, you have medical education, ask me about my feelings, tell me that I need to make blood analysis, then tell me what is the diagnosis
@JonasTeuwen because then 1. you may imagine that you're sick from stuff that you're not sick of, 2. you will argue with them about the diagnosis proving it with the Internet
@JonasTeuwen he told me that I should take some pills of paracetamol, and come after two weeks. Also he told me that I shouldn't worry since Dutch reanimation is perfect
Then he probably thought nothing serious was wrong and it would go away by itself, but that is strange way of saying it.
The doctor at the student health care.
Last time, he kept asking me if I ran into some "risk" (he meant STDs I suppose). I had to convince him I didn't. Then he still give me an address for an anonymous test.
Sure, I understand what happened. But why on earth does he have to expand on that comment again and again instead of just deleting it and posting it as a comment?
Oh, I do like beer, quite a bit, but I don't like the most common Swiss beers: Feldschlösschen, Hürlimann, Calanda, etc too much. They are quite bitter.
@yunone I'm pretty open to any beer, I can't say what I like most. Probably German white beer, I guess, but without Ales and black beer life would be sad...
@tb I can say it about any Dutch city. Even Den Haag, even Rotterdam
even Leiden, unfortunately (
then was so surprising after Sweden - there everything was full of light, green etc. You can walk around everywhere and you relax. Even in the winter when the daylight stops and 3-4 pm it was not as grey
@tb yes, she is. I don't mind: I wouldn't hesitate to tell you that some questions are outside of the scope of the discussion, so ask whatever you want )
It's called the finite intersection property: If a collection of closed sets in a compact space has the property that every finite intersection is non-empty then the entire intersection is non-empty
okay, one good and one bad. now for more sample points...
@Gortaur: I do not recommend the paracetamol after the beer bit... that's a bit hard on the liver. Usually one needs a 12 hour wait in between the alcohol and the paracetamol (assuming normal alcohol metabolism.)
Aspirin however is fine (but of course not too much).
@tb actually that's very kind of them; the idiom I hear is that American beer is nothing different from refrigerated horse piss.
@J.M I know, it's really a lot to ask I think. The more I consider it, the more I think that perhaps Apostol just wanted you to prove the general case as outlined
Question: Prove that a similarity transformation (replacing $x$ by $tx$ and $y$ by $ty$) carries an ellipse with center at the origin into another ellipse with the same eccentricity.
(The next questions go on to prove the same result (and converses) for hyperbolas.)
Please don't feel the need t...
The problem is that rotation has not yet been discussed, so it would put a lot on the reader to just come up with that on their own (not that that's totally outside the realm of possibility)
Maybe I will modify the question to focus more on what Apostol does introduce
@process91: Now I see the problem, but I believe you're overthinking the exercise. I'm pretty sure it was just intended to take the standard normal form and convince yourself that the eccentricity remains unchanged after scaling the axes. I don't think you miss anything.
@tb I hope so, and it is entirely possible that I'm overthinking it. Intuitively, it seems like I can just say "given some central conic, align your coordinate axes with the origin at the center with the x-axis parallel to the major axis" and go from there, but I thought perhaps to be rigorous I should justify why doing so would not change the eccentricity
@tb the next question asks to prove that if two concentric ellipses have the same eccentricity and major axes on the same line that they are related by a similarity transformation, which is also easily reduced to the standard form by this approach.
@JM I suppose the next problem is not so easy, however - it says to show that the Cartesian equation which represents all conics of eccentricity e and center at the origin to prove that these conics are integral curves of the differential equation y'(e^2-1)x/y
@JM I see, from your equation (ax^2+bxy+cy^2 = 1) that this is the equation I'd want to use, but the book didn't provide that and I don't see how to get the answer to the above without deriving that equation
So perhaps I am supposed to dive that deep?
I've probably wasted more time thinking about whether it's really that deep a question than if I just did it already...
Actually in the derivation of ax^2+bxy+cy^2 that I remember, the prerequisite was to show that if the more general conic was in fact a parabola (which can be shown if you were already introduced to the discriminant), there are necessarily linear terms...
...that requires the judicious application of completing the square.
Let me see if I can find the book I know online...
Oh, I'm giving Matt a hard time, recently. But I really find his "prose" so hard to understand that it is difficult for me to tell whether he understood things right, or whether he hides his confusion behind pseudo-formality. Could you have a peek at the comments to his answer?
Well, at first reading it looks to me that he's partially muddled and partially not used to the usual standards for this sort of thing. (I was tempted to say "lazy", but that's too presumptuous methinks.) That's my reading of him anyway...
As long as he's not chafing at your nudges, it should be fine.
That's my reading of him, too. However, I feel like he's sort of cheating his way through the course. He seems to have difficulties of keeping his assumptions separate from the things he wants to conclude. In outline the argument is okay, but there are quite a few mistakes in the details.
"keeping his assumptions separate from the things he wants to conclude." - my experience was that's an ailment that can't be easily cured. It will require Arturo-level patience to treat this properly...
Yeah, some problem with that is: 1. I lack that kind of patience, 2. I can't encourage him without having a basis to do so, and he seems to need encouragement quite desperately...
Well, probably it would be more efficient to suggest we meet IRL, then I could use his reactions to fine tune my carrots and sticks. It's a bit difficult doing that sms-style in comments.
Well, I'd be interested in seeing many of them. It would probably be quite surprising to compare the real life personalities with those they represent here.
xxx: decided to make my skills higher. what would you advise from martial arts? yyy: to pose or for the self-defense? xxx: for the self-defense yyy: jogging zzz: jogging ttt: jogging
111 do you know what helps when you meet zombie? 222 what? 111 jogging
@JM: I just saw joriki's comment to your ellipse. Maybe it's an apple thing. Even after rebooting, and clearing the browser's cache your animation doesn't display properly.
story in the same topic. Moscow Phystech is situated like 200-300km from Moscow, close to a small city Dolgoprudny. Once in 80s students discovered that locals use to meet students at the nighttime and beat them. Students decided to reply to these actions and make some student bands patrolling neighborhoods of the University in the evening. To understand who is the person they meet they ask him to calculate indefinite integral very quickly.
as appeared, they reduce the number of attacks from locals and also that semester all students showed much better in calculating integrals. Maybe a legend, but one prof. from that university told it me quite seriously )
Question: Prove that a similarity transformation (replacing $x$ by $tx$ and $y$ by $ty$) carries an ellipse with center at the origin into another ellipse with the same eccentricity.
(The next questions go on to prove the same result (and converses) for hyperbolas.)
Please don't feel the need t...
