Dave

Clues Since there's been little in the way of proofs, I thought I'd post some clues here to kickstart it a bit. Problem 1: Try considering an isoceles triangle with angles 72, 72 and 36. Problem 2: The secret to integrating this beast lies in splitting the fraction up.

it's not nice. but they are pretty, you can work out all kinds of stuff with them (like arcsin(2) or whatever).

clearly english beer > *

In fact, to further expand on this, take for an example (in a simplified case), a rocket being launched, which loses mass over a period of time. ignoring changes in gravitational field strength, relativistic effects etc, the problem stands that you effectively have a particle with changing mass. in order to create the mathematics behind this, you have to consider the change in mass of the rocket over a "small" period of time. in this case, you then take the limiting value of this small period of time. this enables you to solve the equation that you perform. without the limiting values and calculus in general, you wouldn't be able to do this problem or anything like it. same thing applies for things like shock absorbers (damped harmonic motion), springs, coils, etc. basically, calc is good and kindof essential

it's the concept of a limiting value that's key to calculus. it enables us to find gradients of graphs at any given point exactly and to find the area defined under a graph (which is useful for velocity-time graphs, to quote a simple example). it's a key role in more or less any part of mechanics and if you deal with motion in general then you're going to run into it at some point.

Amendment: there must be a proof behind the answer given. A stated answer will not count. Sorry for the misunderstanding. Also, the answer does not have to be in degrees for the second part of the challenge.

At last, the first problem! Your posts will not appear until the competition winner has been announced. Please read the rules thread before posting a solution in this thread. This week, there are two problems (as a bonus ) for you to pit your wits against. If I can't see any correct proofs or people are struggling a lot within a decent amount of time, then I will post a couple of hints here. Problem 1: Trigonometry Values (Angles stated are in degrees.) Calculate the exact value of cos(72), and hence find the value of cos(36)-cos(72). This is a fairly simple question, but a proof is required. It's aimed at the majority of users here. Problem 2: Calculus This is quite a tough calculus question. If you don't like integrations, then don't bother with this one Find :lint: 1/(1+x^4) dx (that is one divided by (x^4 + 1) for anyone that can't interpret the brackets). Have fun! The winners will be announced at 7:00pm GMT on 18th April 2003.

! not that it's hard or anything (i got to about the first paragraph before i got lost)

Well, I think I'm going to go ahead with it anyway; clearly it may help get a few more active members here and that's a pretty good reason. The first one I'll post will be in about an hour's time, and it's a pretty nice question that we were given, which is quite tricky to see, so it makes it ideal for this kind of competition.

bah. i like imubash better

clearly we need that

We switched over a week ago in Britain and I really do wish they would leave it like this. The mornings are pretty bright and there's still decent sunlight until about 7:30pm. If we didn't change it back for winter it would make things a lot better

I'm 17, currently studying to get my grades to get into Warwick University to study maths.

Yeah, that would be good if it could be arranged. From the "general" (I use the term loosely since only about 6 people have voted) concensus it seems like it might be a good idea, so I'll start gathering some questions up and do a couple of trial runs to get some feedback. So if you have some nice challenges that you'd like to see asked, e-mail them to me at mdave@btopenworld.com

Make sure you read all of the question before you start answering it. It's the most important thing you can do at all. Also, write down all of the information you get mathematically. If it says "the rate of change of volume with respect to time is proportional to the time" then you need to write down: dV/dt = kt You'll also find it'll become a lot easier when you write the stuff out in full.

You probably searched for the wrong thing The best thing to search for is "fibonacci sequence" which gave this link at the top: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html It has quite a lot of information so you're going to be able to find something on them. The entire thing revolves around the series of numbers called the Fibonacci sequence. It's a pretty simple little sequence, and a junior school kid could do it. It goes: 1, 1, 2, 3, 5, 8, 13, 21.. and it's pretty simple to see that u(n) = u(n-1) + u(n-2) (i.e. the nth term in the sequence is determined by adding the preceeding two terms). This is a pretty simple series but it does have some astounding connections with nature in general. The majority of them (to my knowledge) come from a number called the golden ratio (phi). This can be obtained from the Fibonacci series pretty easily, but I'll leave you to look that up. This is a brief overview of this series, but that site looks to be pretty good at explaining quite a lot of stuff. I'm not an expert in it myself, but I can tell you that you can find some very interesting things out with the golden ratio itself, and it is a fascinating area to study. (Incidentally, I think it may be more number theory oriented myself, but I'm not quite sure either )

Yeah, my idea (which I failed to point out, sorry) is to make the problems over a diverse area of topics in mathematics. It won't all be simple, but it should be answerable by most people visiting these forums. P.S. clearly answers should be submitted by e-mail, and I'd accept the first correct answer submitted by that person.

1) No: people should be allowed to wear what they want. 2) No: if people eat in classrooms, it tends to make them messy rather rapidly which just seems wrong. 3) No: it's only polite. 4) Yes: but only if they don't have a decent excuse. It's only polite to get the work in for when someone sets it. Have fun with your survey

Since the maths forums have been fairly inactive over the past week or so (I think I've only seen three or four posts), I've decided to see if people would like some weekly (or fortnightly) maths challenges that they can solve. The idea runs something like this: 1) The problem is posted in the appropriate forum for the challenge. 2) People send me their solutions. 3) At the end of the week, I say who "won" and post a solution. It's all a bit of fun really, but I think it would put a bit more life into the maths forums here. Another rule (to make it a bit fairer) is that nobody can win twice in a row. I'd also like to see people submitting their own problems (and preferably solutions ) which would be quite nice. Obviously, the person that submitted the problem couldn't enter the challenge. Anyway, this post is just to see what the interest in this would be like. If you've got any suggestions, please post them so it can all be discussed. Thanks.

Newton invented calculus to solve the problem of gravitational attraction and gravitation force in general, which, on a sidenote is quite astounding. To invent a completely new area of mathematics (and such a diverse branch at that) to solve a problem and then use it to the breadth that he did is a sure sign of genius.

relative to what?

electrical engineering is the main one that i can think of, but there's quite a lot of others. it's also pretty important for various basic things like damped/forced harmonic motion (you can end up with a second order differential equation that requires complex numbers to provide a real solution).

first one, the second one sounds a bit cheezy

yeah, i've not really looked into C++ gui programming because really i don't need to atm, and it looks pretty nasty. using something like gtk+ is pretty good (since it's fairly easy to produce an interface), but i've yet to look at it properly. but if you're starting programming, definately VB.

i think it will definately need an international effort. a project of this scale is vastly expensive, and although the technology exists, it also has a lot of risks. i reckon it would be a much better idea to wait until the ISS is finished, and maybe use this as some kind of launching platform. i agree though that we'll probably be there by 2020. 2010 is a bit optimistic.