by **Bigtone53** » Mon Jan 21, 2008 12:27 pm

If the ladder extends up the y-axis to infinity, then adding another 'step' at the bottom will not change the answer.

If the resistance between (0,0) and (0,1) is R, then adding the additional step gives the R between (0,-1) and (1,-1) as a parallel of 1 between (0, 0) and (0,1) directly, and a series of (1+R+1) between (0,1) and (1,1) via the y=1 'step'.

R = 1 in parallel with R+2

= (R +2) / (R+2+1)

= (R+2) / (R+3)

R²+3R = R + 2

R² +2R -2 = 0

R = (-2 ± sqrt(4 +8)) /2 = Sqrt3 - 1