Approximations for π and Continued Fractions

The shortest approximation for π is simply 3. This is 4.5% away from the true value of π and in fact this approximation occurs twice in the Bible (see page 169). The longest approximation is 206.1 billion digits long and is still not entirely accurate. Only when we write “π” for π1, are we entirely accurate — everything else is longer and either more or less of an approximation.