Math Game

[KrazyHorse]

You can show that the "jumps" in the numerator happen in such a way that you always get two terms of value 2^(-n) for n>1 and one oddball term of 2^0

[KrazyHorse]

Don't worry; I spent the better part of an hour doing this just now.

[MasterBob The Elder]

[QUOTE] Originally posted by Ramo
y'(x) = 21x^6 - 20x^3 - 6x
y''(x) = 126x^5 - 60x^2 - 6
||y''(5)/|| = too much arithmatic

Is it my turn yet? [/QUOTE

Unfortunately, looks like youy did not pass Calc III, that is not the way to kind kappa, the value of the curavture of a line.]

[SnowFire]

I got like a 35 (out of possible 120) when I took it, and I was 2nd highest at McGill.

Darn. You get at least my congratulations... I took the stupid thing Freshman year when I was a lot more arrogant then I am now, and unsurprisingly got the most popular score on the Putnam, the good old zero.

Anyway, I've got a few questions for everybody, except that my Geometry teacher probably wouldn't approve of me posting questions from the take-home test before I hand it in. Anyway, the problem that should have been the easiest is probably the most annoying right now... a stupid little proof in projective geometry about some points being collinear, and it's such a problem that you don't even have to be inventive with placing points you know the coordinates of and using variables. It's just straight calculation with numbers, and it ISN'T COMING OUT! In fact, the solution keeps getting worse and worse. It started out with of the 3 points, two of the lines between them were the same. I made an adjustment after discovering one mistake, and there were still 2 lines the same. And after finding yet another one (or possibly 2), I now have 3 completely different lines going between these points.

Anyway, here's an enjoyable little problem: Does there exist such a function that f(x) is rational on every irrational number and irrational on every rational number? If there is, give an example, if there isn't, explain why.

[loinburger]

Originally posted by SnowFire
Anyway, here's an enjoyable little problem: Does there exist such a function that f(x) is rational on every irrational number and irrational on every rational number? If there is, give an example, if there isn't, explain why.

Are we allowed to make it piecewise, and/or discontinuous?

[SnowFire]

Argh, I should have mentioned that. It's continuous. Otherwise, the answer is obvious (let x be 0 for all irrational numbers, e for all rational numbers).

[Ramo]

Unfortunately, looks like youy did not pass Calc III, that is not the way to kind kappa, the value of the curavture of a line.

What am I missing? Does the speed of the parametrization have to be constant? Sorry, we didn't spend any time on curvature in my vector calculus class (calc 4; calc 3 is usually Diff. Eq). It's too trivial.

[loinburger]

Originally posted by MasterBob The Elder
Unfortunately, looks like youy did not pass Calc III, that is not the way to kind kappa, the value of the curavture of a line.

Ha ha, I got an 'A' in Calc III four years ago and now I couldn't find kappa to save my life. Hell, I didn't even remember that the curvature was called kappa. Nowadays if I need to find an arc length or an integral or whatever I just write a program to do it; computer science has made me incapable of doing math.

[Ramo]

Solve this differential equation for r:

r''(t) = -C*r(t)/||r(t)||^3

[shade]

something like

r³=6*(-C*(t²/2))
(after 2 ruf integrations)

maybe you like this one:
create 24 by using +,-,x,:
and the numbers 1,3,4,6
You may only use the numbers 1 time each and you have to use them 1 time each.

have fun

Shade

[Roman]

Originally posted by uncle_funk
Answer to mine:
n^2 - (n - 1)^3

I believe this is incorrect. It breaks down at the second term, since using this equation, you get 3, rather than 5, which is the term you put down.

I think the correct equation would be:

2*([n-1]^2 + n) - 1

[Roman]

The other math problems are somewhat beyond my math ability.

[Juggernaut]

Hehe, I altered it slightly to see if anyone noticed.
Correct answer: n^2 + (n - 1)^2

yet your works too...

[Buck Birdseed]

Okay, this is vaguely irrelevant to the game (which I do not wish to participate in), but I was wondering about this the other day: What would be the ultimate shape of a bowl/glass? Imagine you only have a certain amount of material and for simplicity's sake the thickness of the walls of the container would be uniform, what shape would be able to hold the greatest amount of liquid considering a downward gravitational pull? I'm assuming it'd be circular from the top, so to simplify, what shape given a certain length of wire would give the greatest area to the shape contained by it, if you were allowed to keep the top of the shape open? And why?

[KrazyHorse]

A sphere has the most efficient volume/surface area ratio.

You can prove this locally (show it must have constant Gaussian curvature), but it requires a pretty decent knowledge of differential geometry. There might be an easier way to prove it, but this is the method I've seen.

Hmmm...

for the top of the item open, I'm not sure...

Let me think about it for a few seconds.