"PIVOT!"

PIVOT! History & Background Explanation of Mathematics Significance & Application References

"PIVOT!!!" an Introduction

One of the most iconic scenes from the popular sitcom "Friends" is that where characters Chandler, Ross, and Rachel are attempting to move an extremely wide couch through a fairly narrow staircase. The scene is most memorable from Ross yelling out "PIVOT" repeatedly to try to get Chandler and Rachel to rotate the couch around a beam, however the couch is too wide and long to rotate around that point. Simple math and knowledge of transformations would have helped the characters understand that no matter how they rotated the couch, it would not fit going up that staircase. Ross attempted to draw a diagram showing how to move the furniture, but failed. In the end the characters resort to cutting the couch in half and moving it up the stairs which renders the couch useless. So the question is, was there a way for the arguably best three characters on FRIENDS to move the couch up the stairs without cutting it?

Click here to watch the scene from FRIENDS


This is the basis of the transformation and isometry discussion. One of the most basic taught lessons in our geometry classes growing up, is that there are three different ways to move points and objects around a 2 dimensional plane. Those are translations, rotations, and reflections. Each of these are defined differently and result in different positions on the plane, they are all isometries that result in an image from a pre-image. However we know that any two isometries result in a singular isometry, as we work together to discover these solutions we can see that the combining of two isomotries will always be a singular isometry. Refer back to Chandler, Rachel, and Ross to show them our knowledge of isometries.


So returning back to Ross, Rachel, and Chandler, was Ross's notion of pivoting the couch the most optimal way to get the couch up the stairs? It is hard to say without correct measurements and information, however just from watching the clip it looks possible to move the couch or translate it between two of the poles and then flip it on its side. When we are dealing with three-dimensional movement it can be difficult to compare to the two dimensional coordinate plane, but with some simplification the same idea could be achieved. The fact of the matter is while Ross may have thought rotating the couch around this pole was the best solution, in the end there may have been several different ways to get the couch up those stairs and not destroy the couch in the process. Ross if you are reading this paper, please keep going so you too can understand the beauty of isometries and how maybe yelling "PIVOT" was not the best solution to your problem.