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 2009-03-29, 13:21 #1 davieddy     "Lucan" Dec 2006 England 194A16 Posts Find the resistance between A and B Equilateral triangles are inscribed ad infinitum by joining the midpoints of the sides of the previous one. They are made of wire with resistance r per unit length. Attached Thumbnails
 2009-03-29, 22:01 #2 Orgasmic Troll Cranksta Rap Ayatollah     Jul 2003 641 Posts just to see if I have the right idea of calculating resistance, if the following diagram has 1 ohm of resistance on each segment, is the total resistance from A to C 5/6? Attached Thumbnails
 2009-03-29, 22:19 #3 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts B and D are on the same potential, so there's never any current between them. The resistance is still 1 Ohm from A to C. Alex
 2009-03-30, 01:11 #4 davieddy     "Lucan" Dec 2006 England 2×3×13×83 Posts This wasn't supposed to turn into an elementary physics lesson, but in the vein of the last posts, it is worth noting that for the purposes of the question, the midpoint of AB could be isolated from the inner triangles.
 2009-03-30, 01:57 #5 frmky     Jul 2003 So Cal 3×5×137 Posts Hmmm. I did a few cases, using symmetry to simplify the calculations, and ended up with resistances (in units of ar) of 2, 5/4, 28/23, and 79/65 in parallel with the straight section from A to B. These lead to total resistances of 2/3, 5/9, 28/51, and 79/144 between A and B. Definitely converging, but to what I'm not sure.
 2009-03-30, 02:55 #6 wblipp     "William" May 2003 New Haven 236010 Posts 0.535ar Details available upon request if it turns out to be correct. William
 2009-03-30, 06:16 #7 Visu     Nov 2006 Singapore 7510 Posts ar, the length from A to B (a) multiplied by the resistance per unit length r.
 2009-03-30, 07:03 #8 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 242D16 Posts Too easy. Go on to the infamous google labs problem depicted in [URL]http://xkcd.com/356/[/URL] "It's fun! Physicists are two points, mathematicians three." (sqrt7-1)/3 ~= 0.54858... Last fiddled with by Batalov on 2009-03-30 at 07:55
2009-03-30, 09:41   #9
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by wblipp 0.535ar Details available upon request if it turns out to be correct. William
You expect me to work it out?

I know how to do it in principle.
Meanwhile Batalov doesn't quite agree.

I have every confidence in you William, and am definitely
sure about the ar bit of it.

Last fiddled with by davieddy on 2009-03-30 at 09:48

2009-03-30, 09:51   #10
davieddy

"Lucan"
Dec 2006
England

2·3·13·83 Posts

Quote:
 Originally Posted by Visu ar, the length from A to B (a) multiplied by the resistance per unit length r.
In parallel with something a bit trickier.

2009-03-30, 10:59   #11
davieddy

"Lucan"
Dec 2006
England

2×3×13×83 Posts

Quote:
 Originally Posted by davieddy and am definitely sure about the ar bit of it.
Nudge nudge, wink wink, this was a hint folks.
No I don't come from Purley, although like that Jacqui minister
woman, I do share some partiality with "Photography" (geddit?)

David

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