What is the moving sofa problem?

Have you ever watched someone try to squeeze a giant, comfy sofa around a tight corner? It is tough! People yell "Pivot!", push, pull, and sometimes get totally stuck. But did you know this everyday annoyance is actually one of the most famous geometry puzzles in history? It's called the moving sofa problem! Back in 1966, a mathematician named Leo Moser wondered: what is the absolute biggest flat shape you can slide down a straight hallway and around a sharp right-angled corner? A simple square works, but smart mathematicians realized curves are even better! One mathematician even created a giant shape that looks exactly like a chunky old-fashioned telephone. Then, Joseph Gerver calculated a mind-bending sofa made of 18 perfectly stitched curves that spins and slides through a corner in a beautiful, twisting dance! But the wildest part? For over thirty years, nobody could prove if Gerver's shape was the absolute biggest possible one. It wasn't until 2024 that a young mathematician named Baek Jin-eon finally solved it, writing a brilliant proof over 100 pages long! Join Mira and Finn to uncover the brain-bending puzzle hiding in every hallway!