Take another look at the two boards that are used to access Stella's Fishpond, which first appeared in no. 1000.53; also see the figure below. Just how short can the two boards be to reach across in the way shown here, idealized as simply two line segments? That is, what is the length of these two segments?

## Solution

The longer segment is the diagonal of a square of side $2$m. As such it's length is $2 \sqrt{2}$. The shorter segment is half a diagonal so it's length is $\sqrt{2}$.