20090329, 13:21  #1 
"Lucan"
Dec 2006
England
1100101001010_{2} 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. 
20090329, 22:01  #2 
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?

20090329, 22:19  #3 
"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 
20090330, 01:11  #4 
"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. 
20090330, 01:57  #5 
Jul 2003
So Cal
11^{2}·17 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.

20090330, 02:55  #6 
"William"
May 2003
New Haven
2^{3}×5×59 Posts 
0.535ar
Details available upon request if it turns out to be correct. William 
20090330, 06:16  #7 
Nov 2006
Singapore
113_{8} Posts 
ar, the length from A to B (a) multiplied by the resistance per unit length r.

20090330, 07:03  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2438_{16} 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."
(sqrt71)/3 ~= 0.54858... Last fiddled with by Batalov on 20090330 at 07:55 
20090330, 09:41  #9  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Quote:
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 20090330 at 09:48 

20090330, 09:51  #10 
"Lucan"
Dec 2006
England
14512_{8} Posts 

20090330, 10:59  #11 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 

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