[HN Gopher] The Algebra of an Infinite Grid of Resistors
       ___________________________________________________________________
        
       The Algebra of an Infinite Grid of Resistors
        
       Author : gone35
       Score  : 45 points
       Date   : 2025-06-15 05:47 UTC (17 hours ago)
        
 (HTM) web link (www.mathpages.com)
 (TXT) w3m dump (www.mathpages.com)
        
       | ColinWright wrote:
       | See also: https://news.ycombinator.com/item?id=44279181
        
         | srean wrote:
         | Thanks for pointing towards this treasure trove of a website.
        
       | fh973 wrote:
       | See also: https://xkcd.com/356/
        
         | glial wrote:
         | And the Google talk:
         | https://youtu.be/zJOS0sV2a24?feature=shared&t=858
        
       | Koshkin wrote:
       | > _we imagine injecting 1 amp of current into a single node_
       | 
       | I have always had a problem with statements like this. Current is
       | a (measurable) property of an edge, not a node (vertex). One
       | can't "inject" current into "a single node."
        
         | teraflop wrote:
         | By definition, an edge connects two nodes. So clearly, "inject
         | current into a node" is just shorthand for "inject current
         | along a (real or hypothetical) edge leading to a node". This is
         | very common terminology in electronics.
        
           | Koshkin wrote:
           | Sure, but wouldn't it be clearer if they talked about a
           | specific edge? Because there can be several edges leading to
           | a node. (Or, are they talking about, say, all of the
           | "inbound" edges taken together?)
        
             | duped wrote:
             | Thats equivalent according to KCL - I think the equivalent
             | model is "connect a current source I from ground to a
             | node." Thats equivalent to saying "imagine the sum of all
             | currents through edges was -I"
        
         | gus_massa wrote:
         | I imagine you are using an imaginary wire that is perpendicular
         | to the grid and is not shown in the graphics. (Like a
         | multimeter probe.)
        
       ___________________________________________________________________
       (page generated 2025-06-15 23:01 UTC)