Most irrational number

Some numbers can’t be written down exactly in decimal form – doing so would take an infinite number of digits. Such numbers are known as "irrational". The geometric constant Pi and the square root of 2 are both examples. Even though they can't be specified exactly, irrational numbers can be approximated by rational fractions – for example, Pi is roughly equal to 22/7. Mathematicians have come up with measures for how well an irrational number can be approximated this way. These measures reveal that the most irrational number, i.e. the one for which rational approximations perform the worst, is 1 plus the square root of 5 all divided by two – a figure roughly equal to 1.618. This number is already well known. It’s called the "Golden Ratio". Shapes with side lengths in this proportion tend to be especially pleasing to the eye – a fact that was known to painters, sculptors and architects dating right back to the 5th century BC. Mathematicians are yet to understand number theory well enough to shed light on why this number in particular is the most irrational.