Pi Day

What the day is

Pi Day is observed on March 14, because the American date format renders it as 3.14. It is not National Pie Day, which falls on January 23 and involves pastry.

Origin and background

Pi is the ratio of a circle's circumference to its diameter, and it is the same for every circle, which is the fact that makes it worth a name.

It cannot be written exactly. Johann Lambert proved in 1761 that pi is irrational, meaning it cannot be expressed as one whole number divided by another, so its decimal expansion never terminates and never settles into a repeating pattern. In 1882 Ferdinand von Lindemann proved something stronger, that pi is transcendental, meaning it is not the solution of any polynomial equation with whole-number coefficients. That second proof settled a problem that had been open since antiquity: squaring the circle, constructing a square of equal area to a given circle using only compass and straightedge, is impossible, and Lindemann's result is why.

The pursuit of digits is mostly recreational. Practical work needs very few: around fifteen decimal places is sufficient to calculate the circumference of the solar system to within the width of an atom, and space agencies use far fewer than the trillions now computed. Long digit calculations survive as benchmarks for hardware and algorithms rather than as mathematics.

Pi also turns up where no circle is visible, in probability, in statistics through the normal distribution, and in physics, which is the genuinely strange thing about it.

A minority argue the constant should have been defined as the ratio to the radius rather than the diameter, which would make many formulas tidier, and they mark their own day in June.

How to take part

• Measure a circular object's circumference and diameter and divide one by the other.
• Learn why fifteen digits is more than any engineering problem needs.
• Read what transcendental means and what it ruled out.
• Eat a pie, which is the pun the day has fully embraced.
• Note that it is not the pastry day in January.