Here's a little math/physics problem I just ran into with some house maintenance:
Suppose you want to hang a heavy picture/mirror in the center of a wall. However, the studs are not arranged in a way that the center of the wall is backed by a stud.
Assume the picture frame is larger than the $16$ inches between the studs, and assume the frame has a perfectly flexible string behind it connecting to the vertical center of both sides and leaving a half picture height of slack.
How much lower should the nail in the stud farther from the center be in order to center the picture horizontally on the wall?
Best Answer
The nails can be at the same level if you can keep the string from sliding. In the below picture the heavy lines are studs. The light three piece line is the string. $a$ and $b$ are chosen to center the picture on the wall. The total length of the string is $\sqrt {a^2+c^2}+16+\sqrt{b^2+c^2}$ so by measuring the length you can find what $c$ will be to allow you to choose how high to put the nails.