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The Algebra of an Infinite Grid of Resistors

The Algebra of an Infinite Grid of Resistors In a previous note we discussed the well-known problem of determining the resistance between two nodes of an “infinite” square lattice of resistors. The most common approach is to superimpose two “monopole” solutions, one representing the field for one amp of current entering a given node and flowing “to infinity”, and the other representing the field for one amp of current being withdrawn from a given node flowing in from infinity. If the two nodes

Infinite Grid of Resistors

Infinite Grid of Resistors Remain, remain thou here, While sense can keep it on. And, sweetest, fairest, As I my poor self did exchange for you, To your so infinite loss, so in our trifles I still win of you: for my sake wear this... Shakespeare There is a well-known puzzle based on the premise of an “infinite” grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below. Between every pair of adjacent nodes is a resistance R, and w

The 5 Best Griddles and Flat-Top Grills of 2025, Tested and Reviewed

Photograph: Matthew Korfhage Griddle seasoning is, quite simply, protection for your griddle. When a thin layer of oil is heated above its smoke point and allowed to cook off atop the griddle and then cool, it forms a polymer that protects the top of the griddle and leads to better cooks. (Some think that griddle seasoning is to help food not stick to the metal. It may or may not add some nonstick properties, but the main purpose is to protect the griddle against rust and other wear.) For the

Air Conditioners Can Actually Support the Power Grid. Here’s How

As summer arrives, people are turning on air conditioners in most of the U.S. But if you’re like me, you always feel a little guilty about that. Past generations managed without air conditioning – do I really need it? And how bad is it to use all this electricity for cooling in a warming world? If I leave my air conditioner off, I get too hot. But if everyone turns on their air conditioner at the same time, electricity demand spikes, which can force power grid operators to activate some of the

Amazon joins the big nuclear party, buying 1.92 GW for AWS

Amazon tapped into an emerging trend this week, one that’s seeing big tech firms buy power from existing nuclear power plants. The tech company will power a chunk of its AWS cloud and AI servers using 1.92 gigawatts of electricity from Talen Energy’s Susquehanna nuclear power plant in Pennsylvania. Amazon is the latest hyperscaler to go direct to big nuclear operators, following on the heels of Microsoft and Meta. Amazon’s deal was announced Wednesday, but it’s not entirely new, instead modify

Instagram will soon let you re-arrange your grid

You don't have to make a huge effort planning Instagram posts anymore so that your profile takes on a certain aesthetic or so that your grid reads or looks a certain way. Instagram will soon (and finally) let you re-order the posts already on your grid. Alessandro Paluzzi, who reverse engineered apps and posted upcoming features online, found an "edit grid" option within Instagram way back in 2022. Instagram didn't say when exactly the feature will be available, but when you do get the edit grid