Happy Pi Approximation Day

Back in March, we (or at least some of us) celebrated Pi Day and in June we (or probably rather fewer of us) celebrated Tau Day.

Today is the turn of Pi Approximation Day.

As I wrote on Pi Day, the mathematical constant π is an irrational number, which means that its exact value can’t be written down as a fraction or a finite decimal expansion.  A decimal approximation that’s good enough for many practical purposes is π≈3.14, which is why Pi Day is celebrated on 14th March (3-14 in ISO date format, without the year).  A slightly more accurate figure is 3.14159 (and beyond that, I’d have to look it up to be sure).

There are, of course, many fractional approximations to π (i.e. ones expressed as a ratio of two integers, aka whole numbers).  Probably the simplest one is π≈22/7.   That’s 3.14286 to 5dp, so it’s pretty close and certainly good enough for everyday use (essentially, any situation where 3.14 or 3.142 is a close enough approximation, which is most of the time in non-high-precision situations).  It’s also, conveniently, today’s date in standard British date format (omitting the year), which gives us another excuse to eat pies and do all the other stuff we do to celebrate our favourite mathematical constant.