The Heretic had a friend with astigmatism who was afraid of hallways because he felt like they were closing in on him. To cure himself he decided to measure the walls of a hallway and prove that they were parallel. He knew the Heretic was good with the latest tools so he asked him to set up a mobile laser-based measuring device with mirrors and other optics and a system processor capable of producing the desired result. The Heretic got a piece of string and some chalk and proceeded to do the proof the way the ancient Greeks did it.
- Cut string #1 to width of hall
- Fold string #1 in half twice and mark the folds to establish 4 quarters of the length
- Cut string #2 to the length of string #1 + ¼
- Tie pencils or chalk to each end of sting #2
- Fold string #2 in half and mark the midpoint
- Layout string #2 at a diagonal from one wall to another
- Tape down or tack the midpoint on string #2
- Use each pencil to draw an arc on the wall
- For each arc, cut string #3 to length of the arc at the endpoints on the floor
- Tape down or tack one end of string #3
- Fold string # in half and tape down or tack the midpoint
- Rotate the free end of string across the arc. If the end of the string matches the line, the arc is a perfect semicircle, therefore the walls are parallel
- By creating the arcs with string #2, you are creating double napped cones cut in half by the plane of the floor.
- A plane is perpendicular to the axis of the cones will intersect the cone to create a circle (as demonstrated by string #3).
- Two planes that are perpendicular to the same line (the axis of the cones) are parallel to each other.
The Greek mathematicians didn't need precise measuring tools. They had precise ideas.