<p>LOL, nice try! You are the one losing the argument, and now I have to solve a problem for you? If you are kind enough to solve my problem, a real simple high school geometry problem, then I might consider spending my time for your problem. Good luck!</p>
<p>Let C be the unit circle x^2+y^2=1. A point p is chosen randomly on the circumference C and another point q is chosen randomly from the interior of C (these points are chosen independently and uniformly over their domains). Let R be the rectangle with sides parallel to the x and y-axes with diagonal pq. What is the probability that no point of R lies outside of C?</p>
<p>Remember, this is a simple geometry problem - should be no sweat for someone as talented as you. I will check back in half hour at 11:20 PM.</p>
<p>Wow…Was that question a joke, or were you serious? I thought you were better than Putnam 200 or USAMO Qualifier? That problem literally took me two seconds man. I knew you were a fluke. You’re not even worth talking to man, go back to your little cave and study some real math. </p>
<p>The answer is 1/2, by the way. </p>
<p>And if you need explanation, don’t hesitate to ask, I’ll be glad to pinpoint your fallacies once again.</p>
<p>4/(pi^2) looks right to me. Integrate |4sin(x)cos(x)/pi| from 0 to 2pi and divide by 2pi since, if x is the angle formed by P, the origin, and the positive x-axis, the probability that Q works is |(2sinx)(2cosx)/pi|. Taking the average value of that function from 0 to 2pi gives an answer of 4/(pi^2).</p>
<p>I was one of the few people fortunate enough to have this ‘dilemma’ of choosing between two or more of the HYPM for an undergraduate education. Two friends of mine made the same decision in their respective years. For each of us, the decision was nearly impossible on paper. Everything looked so similar, and each had their own personal bias toward one school or another. BUT when we visited each campus as ADMITTED STUDENTS trying to figure out where they would like to live and learn for the next four years of their lives, the decision became easy. Instinctive. From the gut.</p>
<p>One of my friends ‘wanted’ to like MIT, but couldn’t help but choose Princeton.
Another ‘wanted’ to like Harvard, but couldn’t help but choose Yale.
I ‘wanted’ to like Princeton, but fell in love with Harvard once I set foot on campus as an admitted student.</p>
<p>As an added aside: seeing schools as elite as Harvard or Princeton as a prospective applicant is vastly different than seeing them as an admitted student. The two see with different eyes.</p>
<p>I think it’s great you like Princeton so much. My daughter is going to be starting there in the fall. We are all so thrilled she made it in. Now for some tips:</p>
<ol>
<li>Get the top SAT scores you possibly can – 2010 will be the first year college applicants don’t have to have all of their SAT scores sent. Take the test as many times as you need to.</li>
<li>In order to get the top scores – take a prep class. The only people who don’t need prep classes are people who score at least 2300.</li>
<li>Take as many AP tests as you can…did you know you don’t have to take an actual class in order to take the AP test? You can do it on your own…go for it!</li>
<li>Make sure you are the best in whatever “passion” you have. If you’re a runner – get regional and national awards. If you’re in drama…make sure to get the leads in plays; write your own plays; blog about plays; write articles for your school paper and interview celebrities…you get the idea. </li>
</ol>
<p>The Ivies only want people who are the very best in whatever category you claim to be your passion area. Write all of your essays about something related to your passion. Make sure that people who write your recommendations know which passion you are marketing.Go on campus tours; write to the admissions office; make a great impression without coming off as desperate or fake.</p>
<p>razorrazor and FightTheTide11 are absolutely correct. Nice.</p>
<p>sirgawainknight: The argument was already over in the previous pages. Fermat tried to turn the tables by changing the subject but as you can see, it didn’t work out for him.</p>
<p>Congratulations on the new U.S. News rankings. I saw that The Daily Princetonian carried it as a breaking story and even the official Princeton University website crows about it.</p>
<p>Of note, they completely neglected to mention that the top ranking was shared with another school.</p>
<p>“The latest college ranking conducted by U.S. News & World Report has listed Princeton University as the top school for undergraduate students”</p>
<p>“The University was ranked No. 1 in the Best National Universities category in “U.S. News 2010 America’s Best Colleges” by U.S. News & World Report”</p>
<p>Meanwhile, the Crimson and the Harvard U. website completely ignored the rankings, as is usually the case.</p>
<p>Wow Princeton, that’s a little disingenuous as well as unclassy to carry a pretty long feature story about being ranked the #1 by USNWR without even mentioning that it was a tie for first.</p>
<p>I might have expected something like that (or maybe some tongue in cheek humor instead) from the Daily Princetonian, but that was from the University itself.</p>
<p>Oh Ske, I see a bit of vitriol flowing. It would have been wiser, however, to check Harvard publications before making your claim. You must not read them very frequently. The Crimson, the Harvard Gazette and Harvard Magazine (all of which I peruse as an alumnus of the law school) regularly report on all awards for and recognitions of Harvard and its students. Every school does. There’s nothing unique to Princeton here (though I do agree that the news story should have mentioned the tie) and there is little if any doubt that the Crimson will report on the U.S. News ranking this year just as it has in previous years. Sanctimoniousness is unbecoming.</p>
<p>As for the use of the word “crow” I suspect you reserve that for Princeton and refer to Harvard’s stories simply as “reporting”. I would repeat what I always say, that the differences in quality among these top schools are minor, but I suspect that would just irritate you.</p>
<p>Well, I do concede that I was wrong about the Crimson story, but it wasn’t there when I checked it last night. On the other hand, the Daily Princetonian was all over it even before the official results were announced (fully 2 days ahead of the Crimson). </p>
<p>Yes, although they both “reported” the story, the tone is markedly different. The Princeton U. and the Daily Princetonian stories (with 20 readers’ comments) are ecstatic and self-congratulatory, while the Crimson story’s tone is very matter-of-fact (with zero comments). The title of last year’s story was “Harvard Tops Princeton, but Students Dismiss the Rankings”.</p>
<p>Harvard Magazine is not an official Harvard University publication; it is produced by the alumni and is editorially independent. I don’t believe the Harvard Gazette, which is an official publication, has ever run a story specifically about U.S. News College rankings, although you may occasionally find some very brief mention of its graduate school rankings. It’s all very subdued, and certainly nothing like what you saw on the official Princeton website yesterday. Pretty embarassing stuff. </p>
<p>Contrary to what you claim, I think the Gazette will ignore this year’s College rankings, as it has in the past years.</p>
<p>Personally, I prefer Harvard’s coverage because it is much more tasteful. It’s one thing to crow about student’s accomplishments and awards, and something else entirely for a supposedly leading university to find validation in arbitrary and flawed rankings by a second-rate newsmagazine.</p>
<p>Well Ske, I see this really has gotten under your skin. Your “concession” is accepted . . . however grudging it might be. As for the rest of your analysis, you don’t suppose there’s a little bias in the eye of the beholder, do you?</p>
<p>
</p>
<p>The Daily Princetonian story appeared late Wednesday evening after the official announcement had been made by U.S. News and reported to the wire services. The Crimson story appeared just slightly more than 24 hours later. Do we get another concession?</p>
<p>
</p>
<p>There’s no difference in “tone” whatsoever. Both stories are nothing if not matter-of-fact and most of the comments appended to the Daily Princetonian story are intentionally ironic, actually critical or clearly written by individuals not associated with Princeton despite their screen names. One, in fact, sounds vaguely familiar.</p>
<p>
</p>
<p>Any idea who reader “2012” might be?</p>
<p>The Crimson reporters, on the other hand, dug deeper to prove that a “tie” is not really a “tie” and that Harvard should have been ranked higher.</p>
<p>
</p>
<p>But really, Ske, I do think you go a bit too far.</p>
<p>
</p>
<p>Heck, I’m going to have to go back and re-read the fine print on my Princeton diploma. I must have missed that word “supposedly”.</p>
<p>Lighten up my Crimson friend. You’re taking these rankings, your alma mater and even, dare I say it–yourself–too seriously.</p>
<p>If you are between the two, I would go for Harvard. It is the oldest university in the country, meaning much more history then the rest, it is in a suburban area (Cambridge) but convinently located near Boston for a big-city feel. Besides, Harvard is very rigerious (why do you think that it is still #1 although tied with Princeton) and has been #1 for many many years?<br>
If you are open (and I would apply to much more than just Harvard or Princeton) open up to Yale. Although Princeton seems better, I think Harvard and Yale are better, and if you should choose between two, it would be those. But, it is all your choice. </p>
<p>I hope I helped, and if you really want to go to Princeton, I am not stopping you, but I would choose Harvard. Check out their website. It is cool. Also look into Yale. You may like it.</p>
<p>Sorry about that 4th house, i guess I was mis-informed. I just thought since it was coincidered a suburb of Boston, but now I think of all the suburbs of my city and how some of them seem somewhat urban, and i now rethink</p>