Question

A foreman asks if thefloor and ceiling are parallel. The carpenter nails the center of a straight beam to the center of a post then rotatesthe beam, and as it hits the ceiling, it hits the floor. How does this show the floor and ceiling are parallel?

Answer 1

When the carpenter nails the center of the straight beam to the center of a post and rotates the beam, it creates a scenario where the beam is always perpendicular to the post at its center. This means that as the beam hits the ceiling, it is parallel to the floor.

Let's break down the reasoning behind this:

1. Initially, the beam is straight and perpendicular to the post at its center.
2. When the carpenter rotates the beam around the nail at its center, the perpendicularity of the beam to the post remains unchanged. This is because the point of rotation (nail at the center of the post) is also the center of the beam.
3. As the carpenter rotates the beam, the part of the beam that touches the ceiling remains parallel to the floor, and the part that touches the floor remains parallel to the ceiling. This is because the perpendicularity to the post is maintained throughout the rotation.
4. Since the beam hits both the ceiling and the floor at the same time (when it is perpendicular to the post), it means the ceiling and floor are parallel to each other.

In summary, by rotating the beam and observing that it hits both the floor and ceiling simultaneously, the foreman can conclude that the floor and ceiling are parallel to each other.