moving sofa problem
In Douglas Adams' book Dirk Gently's Holistic Detective Agency the character Richard MacDuff says at one point, "It would be really useful to know before you buy a piece of furniture whether it's actually going to fit up the stairs or around the corner." Mathematicians call this the Moving Sofa Problem and it has been tackled in various forms over the past few decades.
One version of it, formulated by Leo Moser in 1966, asks: What is the largest sofa (in terms of area) that can be moved around a right-angled corner in a hallway of unit width? The sofa can be any shape and doesn't even have to resemble a piece of furniture! The question simply asks for the biggest, unbendable area that can be maneuvered around the corner. Several different approaches suggest that the answer is about 2.21 square units. Variations on the problem involve negotiating pianos and other items around different types of bends and passageways.
1. Gerver, J. L. "On Moving a Sofa Around a Corner." Geometriae Dedicata, 42: 267–283 (1992).