January 17, 2006
Consider a spherical cow, covered in resistors
(Anybody who didn't take an A-level in Physics may as well switch off now. Any readers who sat next to me throughout A-level Physics lessons may wish to consider that it might be their fault I wasn't paying enough attention to be able to work this out. ;-) )
This question's been bugging me for days. I did have an answer, but after a spot of googling showed me I was wrong, I realised I was talking rubbish.
Imagine, if you will, a flat square grid of points, such that every point is connected to the 4 adjacent points by a 1Ω resistor. The grid extends infinitely in all directions. What is the resistance between 2 points on the grid a knight's move apart? (e.g. 2 squares up and 1 across, WLOG) Or, for a simpler starter question, what about between 2 points diagonally adjacent? Or even just 2 adjacent points? (Is that as simple as just 1Ω? My hunch is no.)
Maybe I've missed something while googling for answers to this, but if anyone has a good solution I'd be very interested to hear it! Just to clarify, I have some numerical answers from googling, but I'm far more interested in how they're arrived at than what the actual numbers are.
[Update: Chris has considerably better google-fu than me, and found a solution for the diagonal case. It contains hard maths that I can't really justify spending the time to get my head around in the middle of exam season, alas. There's a paper with even more on this too. Eek!]
Posted by James at 22:59
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lazyweb
maths
electronics
December 22, 2005
Forum software
Oh boy, am I going to regret asking this.
I'm looking for a web application. In particular, I'm looking for web forum software which:
- has a good security track record. I know no software is 100% secure (fuck off, DJB), but I don't want to use phpBB,
- is simple enough for a numpty like myself to configure and maintain,
- and finally, either offers some kind of gallery functionality, or ideally integrates with Gallery.
Geeklog looks promising, but I'm a bit confused as to whether I should be using version 1 or version 2. PHP-Nuke looks like it does what I want, but I'm not convinced about its security record particularly. Any other recommendations are welcome!
Clarifications:
- Registration needs to be moderated by the administrator of the site, not automatic.
- Image upload to the gallery part of the site, however it's implemented, needs to be available to all registered users and nobody else.
Posted by James at 15:18
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Tags for this entry: lazyweb