davesbird

A lecturer showed me (and the rest of the class) this proof in the middle of a Group Theory lecture. I'm not entirely sure why, but I guess I just saw it as something more interesting than what we were currently covering in the lecture. As to whether it is neat or not, well that would be a matter of opinion, but for me, it was nice to be shown something quick and small, that actually used Fermats' Last Theorem, which as we all know, inspired many to search for a proof.

It's all about the n'th root of 2, and proving its irrationality (where n > 2). Suppose [imath]\sqrt[n]{2}[/imath] is rational. Then [imath]\sqrt[n]{2} = \frac{a}{b}[/imath] for [imath]a, b \in \mathbb{Z}[/imath]. So we must have that [imath]2 = \frac{a^n}{b^n} \Rightarrow a^n = b^n + b^n[/imath]. However, this is a contradiction of Fermat's Last Theorem, so it's irrational for n > 2. Just thought it was really neat.

I can vouch for dave, I sat and watched him do it, and the reason he can get such a high score is cos when he's bored, or just wants to procrastinate about revision he plays chopper challenge to pass the time, hence he's got good.

When you have [math]f^6(0)[/math] this means the 6th derivative of f. It is actually more commonly written as [math]f^{(6)}(0)[/math] to show that it is a derivative of f as opposed to a power of f.

I was looking at the Vedic Maths tutorials last night, and the one i particulary liked was for doing two, (or even three digit), multiplication very quickly: The sutra used here is Vertically and Crosswise: To multiply two numbers think of them as set out as below, 21 x 26 = 2 1 | x | 2 6 --------- 4 (14) 6 --------- Multiply your first column together to get the first part of the answer, i.e 2 x 2 = 4. Then, multiply crosswise, i.e 2 x 6 and 1 x 2, and add these numbers together to get the middle term, i.e 12 + 2 = 14. Then multiply the last column together to get the last part of the answer, i.e 1 x 6 = 6. When you have a number of more than one digit, you carry over as you would in "normal" maths, so here, the 1 from the 14 is added to the 4 at the beginning to give 5 And so the answer in this case is 546.

This is fine for indefinite integrals, which is what I assume you were given, but don't forget that when you have a definite integral, and you make a substitution, you must also change the values you are integrating over, according to how you have done your substituition, For example, if in the question given, you were integrating between 0 and 1, these need to change to 1 and 3, (ie if x = 1 originally then since u = 2x + 1, u = 3)

Yes indeed' date=' multiplying by a negative is the only time when the inequality sign should be reversed. What can become tricky is when you have an equation like [math']\frac{1}{x+2} < 4[/math] In this scenario, you must square the bottom, (and indeed the whole equation) before muliplying up, as you don't know whether [math] x-2 [/math] is positive or negative, ie. continue with: [math]\frac{1}{(x+2)^2} < 16[/math] [math]1 < 16(x+2)^2[/math]

I think you misunderstand, a tsp of sugar works for me, so i'm not looking for a way to make hiccups stop. I was just wondering if there was a medical/scientific reason as to why this method works?

My question is: It has been said that a teaspoon of either sugar or malt vinegar is supposed to clear the hiccups. From experience I have found that it does seem to work, but what I wanna know is if here is any scientific reason as to why this method might work?

Ahhhhh, just the wrong time to bring it back, a week later woulda been perfect. You see, Dave and I are currently in the middle of a week of exams, and the arcade seems to be taking precidence over our revision, so much so, the exam I have tomorrow, I haven't done any work for, and can't seem to concentrate cos all I can think is: must get my post count up so I can join Dave in the fun that is the arcade.

Last year, once the exams were over and I had four weeks of term left, in the beautiful sunshine, I read the ever popular Fermats Last Theorem by Simon Singh. I didn't exactly wan to suddenly start trying to reproduce the proof or anything, but it did get me interested in Elliptic Curves and stuff, and hence has helped me to choose some of my options for next year. Another book, that I won as a Maths prize back at school, was Why Do Buses Come in Threes? which applies maths to everyday situations, which was a good read, if nothing else.