Sofa Moving Problem

or If the Movers Had Been Mathematicians

Simplification

First, let us simplify the problem a little and consider the situation when a pole (of ignorable width but still infinitely heavy) has to be moved around the corner, instead of the sofa.

Look at the GeoGebra dynamic worksheet and try to find out how long the pole could be. Change the length of the pole AB with the slider p. Move the pole by dragging the blue point A, rotate the pole with the green point B. The pole will turn red if you touch the walls of the hallways.

Try to answer the following questions:
1. Can a 2 m pole be moved around the corner?
2. What is the maximum length of a pole that can be moved around the corner?
3. What conditions should be met for the pole to reach its maximum length?

Write down the results and see the answers on the next page.