Shadow

In that case, what would such a function look like?

Hey all, Let [math]M_A[/math] and [math]M_B[/math] denote the masses of objects [math]A[/math] and [math]B[/math], and let [math]R[/math] denote the distance between them at [math]t_0[/math]. Is there any way to calculate the instantaneous [math]F_G[/math] acting upon the two at time [math]t[/math] (from a Newtonian perspective)? What confuses me is that the distance between them changes with the distance traveled, which in turn changes according to the force acting upon the two, which in turn changes according to the distance between the two, and on we go in a vicious circle. What I'm a little afraid of is that I'm touching upon the n-body problem, but I'm not sure, that's why I ask. Cheers, Gabe

Here is what I mean:

If you're asking about the reason behind the name, then I'm not sure, although I guess it's because it "goes on for ever" (ie.: has no minimum or maximum) therefore it's not "closed", but "open". EDIT: Woops, didn't notice the post above )

Here are a couple of nice ones:

He doesn't know either, but they don't think it was a tick, and neither do I...anyhow, thanks for your input )

Not a sting, I would've felt that. Spider or ant were my guesses, but I've been bitten before and it wasn't even close to this. The reason why it surprises me is that I'm not allergic, or maybe haven't been up until now. I was just wondering if this was typical for some kind of insect, I know you have practically no way of telling otherwise. Thanks for your input )

Hey all, I was bitten by an insect the other day. At first it looked pretty much like a regular bite, so I didn't pay much attention to it. However, when I woke up the day after (yesterday) my leg had swollen up from my ankle almost to my knee (the bite being sort of in the middle) and I could barely walk. Since then I've seen a doctor, and he gave me some kind of cream (Flegmoton I think, I've used it before with a chronic big toe infection) which seems to be helping. Then again, I only put it on this morning, but the swelling has diminished significantly since yesterday. What I was wondering is if anyone recognized the bite, or has any idea what kind of insect could deliver such a kick. Here's a link to a couple of pictures I took before my battery ran out: http://img165.imageshack.us/gal.php?g=p1010333.jpg Does it seem familiar? Cheers, Gabe

Whoa, that's a little too sophisticated an answer for me to absorb, but I understand enough to get the gist. Thanks guys )

Something that could be of use due to...recent events )

Hey all, I was wondering, if one were to define a number r, for which [math]|r|=-1[/math], would it be possible to logically deduce it's behavior in mathematical operations? I know that the very concept is unimaginable and I also know it would be useless. But if we can have square roots of negative numbers, why not numbers denoting negative length? I'd be interested to know what [math]r^r[/math] would be, for example. Cheers, Gabe

Have a look at the following: http://en.wikipedia.org/wiki/Turritopsis_nutricula http://en.wikipedia.org/wiki/Hydra_(genus) The former is a jellyfish, and the latter "is a genus of simple fresh-water animals". What's interesting is that both of them are considered biologically immortal. Now, I doubt we could get the brain to revert to a polyp state, so I guess it doesn't have much to do with the OP, but given the thread name I'm hoping it's not completely out of place Cheers, Gabe

I was wondering though, when suffering from a hangover I don't usually get headaches, I get cramps, and no matter how many bananas I eat or how many bottles of "Magnesia" I drink, they don't go away unless subjected to some serious physical activity (which is not all that comfortable at the best of times ). Any idea why this happens/how to get rid of them?

It's not. It's usually a "proof" involving division by zero, or some such nonsense... And I'm not sure this is the right section for this, although I'll leave that to the mods

Hey all, so, I was at this math contest last Tuesday. The contest consisted of 4 question, of which one was geometry. I had absolutely no clue on how to solve it, so I was wondering if anybody here could help me. We have a triangle [math]ABC[/math], which is not isosceles. Let [math]x[/math] be a line that bisects the angle [math]ACB[/math], [math]y[/math] be the perpendicular bisector of [math]AB[/math], [math]h_a[/math] be a line perpendicular to [math]BC[/math] and passing through [math]A[/math] and finally [math]h_b[/math] be a line perpendicular to [math]AC[/math] and passing through [math]B[/math]. Let [math]K \in x \cap y[/math], [math]P \in KC \cap h_a[/math] and [math]Q \in KC \cap h_b[/math]. Let [math]A_{AKP} = A_{BKQ}[/math], where [math]A_{XYZ}[/math] denotes the area of the triangle [math]XYZ[/math]. Determine the size of the angle [math]ACB[/math]. Since my knowledge of English mathematical terms is unsatisfactory at best, I attached a picture in case anyone was confused. Anyway, I already know the correct answer is 60°, but I haven't got the faintest idea why. I don't need the result for anything anymore, but I sure am curious, so thanks in advance for any light shed on this matter. Cheers, Gabe

Correct me if I'm wrong, but doesn't coffee also dehydrate? And if so, isn't it a bad idea to drink coffee while having a hangover?

Does this have a solution? I'm a complete amateur, but if you plug this into an equation, you get [math](a+bi)\cdot(a-bi) = -1[/math] where [math] a, b \in R[/math] [math]a^2+b^2=-1[/math] And as far as I know, there are no real numbers which satisfy this equation...then again, there is the pretty big chance that I'm completely off, so don't take this too seriously... Cheers, Gabe

Here ya go ) (The fun starts at 0:45)

:-D I'll be honest with you, if you solve that one I'll be the happiest person on the planet...

I meant a calculation mistake. And if I understand correctly, the r issue should have no effect since this will be used in a program where r (and therefor F) is constantly recalculated in a loop. Cheers and thanks, Gabe

Hey all, I just need someone to check the following: [math]F_a= G \frac{m_a \cdot m_b}{r^2}[/math] [math]a_a(t)= \frac{F_a}{m_a}[/math] [math]v_a(t)= \int G \cdot \frac{m_b}{r^2} \,dt = G \cdot \frac{m_b}{r^2} \cdot t + v_0[/math] [math]s_a(t)=\int G \cdot \frac{m_b}{r^2} \cdot t + v_0 \,dt = G \cdot \frac{m_b}{2 \cdot r^2} \cdot t^2 + v_0 \cdot t + s_0[/math] Cheers, Gabe

I tried out s=1, and c=1, 2, 3, and all the solutions are complex, so I wouldn't be at all surprised if a=b=c=s was the only solution. Unfortunately I have no clue how to put a restriction on a variable in Maple (any ideas by the way?), and I can't do it by hand for all possible values of c, so I guess I'll never be completely sure. But it's a reasonable estimate, and more than sufficient for my curiosity. Thanks again, Gabe

That last sentence was what I was after. Although I must ask, why won't the following equations yield the correct result? [math]a\cdot b\cdot c = s^3[/math] [math]2(ab+bc+ca) = 6s^2[/math] The positive solutions of these equations are stated above...and while yes, logically the surface and volume of a non-cube cuboid should never be the same as those of a cube, these equations disagree. However, there is the not-so-slight possibility that my equations is just the wrong way to think about it. Thanks for your answers, Gabe

But what if [math]a \neq b \neq c \neq s[/math]?

Hey all, The title's a little misleading, what I'm really wondering about is, can a cube and a cuboid have the same areas AND volumes, without the trivial solution of a=b=c=s, where s is the side of the cube. I did some calculations, however I have absolutely no idea if they're right, and to be quite honest I sort of doubt it. If a, b and c are the sides of a cuboid, and s is the side of a cube, this is what I came up with: http://i44.tinypic.com/oi9e75.jpg Cheers, Gabe