Ever tried packing a bunch of boxes and thought, “There has to be a better way”? 📦 Mathematically, you’re right—and also very wrong. This problem lives in packing and tiling theory, a branch of geometry and optimization that asks how shapes can fill space with maximum density (least wasted area). What’s surprising is that the most efficient arrangement is often not the neat grid your intuition prefers. When you try to pack identical rectangles into a square: • Perfect rows and columns usually waste space • Slight rotations, offsets, and asymmetry can increase packing density • The problem quickly becomes computationally hard (many versions are NP-hard) In fact, mathematicians and computer scientists use optimization algorithms and heuristics (rules that work well but aren’t guaranteed perfect) to search for these weird-looking solutions. These same ideas show up in: • warehouse logistics 🏭 • chip layout and circuit design 💻 • protein folding and materials science 🧬 So whe...