This seems like an incredible magic trick, but once you look closely, it is a magic trick - any series of numbers can be expressed as a constant with this formula.
In a different world, we settled on a system of notation based on continued fractions rather than decimals for writing non-integers. In this world, nobody marvels at the irregularity of pi or e, the fact that they seem to go on for ever without a pattern - both numbers have elegant and regular representations as infinite sums of fractions.
In this world, we all found it slightly harder to make change at the grocery store, but perhaps we made up for that by producing a million high-school Ramanujans.
In a different world, we settled on a system of notation based on continued fractions rather than decimals for writing non-integers. In this world, nobody marvels at the irregularity of pi or e, the fact that they seem to go on for ever without a pattern - both numbers have elegant and regular representations as infinite sums of fractions.
In this world, we all found it slightly harder to make change at the grocery store, but perhaps we made up for that by producing a million high-school Ramanujans.