Recent content by poissonspot

Hi bugatti79, The $r+\rho$ term cancels upon dividing $N_x$ by the length $|N|=\sqrt{|N_x|^2+|N_y|^2}$. As for the second part, Pythagorean and sum-difference identities establish the equality...

Check your answer here: lcm of 3'('2x-2')' and x'('5x-5')' - Wolfram|Alpha

One could tackle it from this direction: First consider the following sum, for a positive function $0 \leq f \leq 1$ $s_n $=$\sum_{k=1}^{2^n} \frac{k − 1}{2^n}.\chi_{E_{n,k}}$ where, $E_{n,k}$=$\left\{x \mid \frac{k-1}{2^n}\leq f(x) < \frac{k}{2^n}\right\}$ $s_n$ are simple functions that...

Here:

When I was first introduced to a derivation of the taylor series representation of the exponential function here (pg 25): http://paginas.fisica.uson.mx/horacio.munguia/Personal/Documentos/Libros/Euler%20The_Master%20of%20Us.pdf I noted the author, Dunham mentioning that the argument was non...

I don't know if I've ever encountered a differential term with a modulus around it (or if I have, ignored it). Here's an example: $ \int\limits_{\gamma}{\rho(z)}{|{dz}|} $ If it was simply $ \int\limits_{\gamma}{|{dz}|} $ I imagine this is the length of the curve $\gamma $, but what might the...

Hi, I wondered whether a well known expression is known that computes the area between two vectors in R^n. By area between two vectors, I mean the area that would be computed by considering the subspace spanned by the two, projecting the entire space to a "parallel plane" and then finally given...

Thanks. I figured that out and edited the first post just before you posted. I did not think that there are infinitely many representations of a non unit fraction in terms of distinct unit fractions and so thought that given one I had the only one that would do so.

I'm afraid I'm being awfully careless in the statement. thank you,

Is it necessary for a unit sum composed of unit fractions to include 1/2? Doing maple runs this seems to be the case, but it is not evident to me how this could be Edit: In fact it seems it could not be, given the Erdos Graham problem Erd?s?Graham problem - Wikipedia, the free encyclopedia But...

Someone I talked to this week wanted to define a function from reals to reals that captured the sense that each negative number has an "nth root" if n is odd. We talked about how the standard definition only applies to positive reals, but considered this case if we defined, for instance...

Hey, What is the greatest number a k-term arithmetic progression starting with 1 can end in if each term is less than or equal to n? I'm looking to write this as an expression involving n and k in order to count the number of arithmetic progressions of length k with each term in $[n]$, that is...

That was exactly what I meant. remember we are first considering the mapping of the "boundary" of the circle, which as you said is a line. If we choose two points other than z=4 on the the boundary then and consider their mappings we should get two points on the line (the line in this case being...

Thanks, this is close to how I approached the problem. I used vector algebra though instead and solved for points where the dot product was equal to zero. btw, I'm still interested in other solutions if anyone else is. Thx again,

I believe what they mean by finite points in this case is points on the circle that do not map to infinity. I think the idea is that since we know the circle is mapped to a line (from this being a Möbius transformation and the point $z=4$ being a pole of $w=f(z)$), we can pick two points on the...