Press "Enter" to skip to content

Approximation with the Mediant

John Cook didn’t make a typo:

Suppose you are trying to approximate some number x and you’ve got it sandwiched between two rational numbers:

a/b < x < c/d.

Now you’d like a better approximation. What would you do?

The obvious approach would be to take the average of a/b and c/d. That’s fine, except it could be a fair amount of work if you’re doing this in your head.

Read on for a separate approach taking the mediant (not median) of the two fractions.