Is It Straight?

What is the best way to hang the mirror so it is straight? Find out from this puzzle.

Mitchell hung a mirror on the wall in his house.

To make sure it was perfectly straight, he measured exactly 40 cm (16 in) from each of two points along the left edge of the mirror to the adjoining wall. But when his wife Luanne walked in and looked at the job, she said, "It's not straight."

"That can't be," said Mitchell. "I know these walls are vertical because I double checked them with a level and with a plumb line. I measured from the left edge of the mirror to the wall in two places, both 40 cm. And I also checked to make sure that the mirror is a perfect rectangle. The wall is vertical. The left edge of the mirror is parallel to the wall. The right edge of the mirror is parallel to the left edge. It's straight."

"Well," said Luanne, "I'm looking at the right edge of the mirror, and it isn't vertical."

Who's right, Mitchell or Luanne?

Course:

Math [1]

Result/Solution(s)

They are both right. It is true, as Mitchell says, that the adjoining wall, the left edge of the mirror, and the right edge of the mirror are all parallel. But Luanne is also right when she says that the right edge of the mirror is not vertical, although she must have very sharp eyes to notice it.

Earth with buildings Vertical means pointing toward the center of the Earth. Let’s say we put up a tall building at the North Pole and another in western Africa, making sure that each is vertical. They are not parallel. Parallel lines are defined as lines that will never meet. If we follow the lines made by these two buildings, they meet at the center of the Earth.

In principle, the right edge of the mirror that Mitchell installed is not vertical if it is, as he says, parallel to the left edge and to the adjoining wall. But, the difference is very slight.

Hmmm . . . How far off vertical is the right edge of the mirror?

Math Puzzle [2]