Lord Rayleigh and James Jeans tried to explain blackbody radiation using classical physics. They failed spectacularly. Their formula worked at low frequencies but predicted infinite energy at high frequencies. This…
Wien's displacement law and Wien's distribution law are fundamental to understanding blackbody radiation. This guide covers both formulas, their derivations, and how they predict the relationship between temperature and peak…
Here's a mathematical fallacy that trips up even sharp students. Can you prove that the derivative of x squared is x instead of 2x? I'll show you the flawed proof,…
Ramanujan's nested radical problem looks impossible at first glance. Infinitely many nested square roots, each multiplied by increasing integers. How do you evaluate that? I walk through the solution step…
The Eagle Nebula holds one of space's most intriguing mysteries. High-powered telescopes have captured images revealing what appears to be a human figure within the gaseous pillars. Is it a…
Rivers sustain civilizations, but we're killing them. From the Yangtze to the Ganges, the world's most endangered rivers face pollution, damming, over-extraction, and climate change. I've documented 20 rivers on…
The universe is staggeringly vast. Stars account for 98% of matter in a galaxy, and there are trillions of them out there. This introduction covers star types, stellar evolution, galaxies,…
Not all pollution glows in the dark, but radioactive pollution is uniquely dangerous. It contaminates land, water, and air with unstable atoms that emit harmful radiation for decades or centuries.…
Chemistry has a dark side. Some of history's greatest chemists paid the ultimate price for their discoveries. From Karl Scheele tasting every compound he discovered to Marie Curie's radiation exposure,…
