Behind the number that begins three point one four and never ends, there are stories that usually go unnoticed. I'm gathering them here.
Ongoing3 facts
01
The 35 Digits Carved Into a Tombstone
Digits computed 35
In 1610, Ludolph van Ceulen died after spending much of his life chasing a single number. What he was after were the decimal digits of pi. He used a method that approached a circle by steadily increasing the number of sides of a polygon, and in the end he reached 35 digits. The number of sides he needed to get there was staggering. This calculation, which took years, was done entirely by hand in an age when nothing existed beyond pen and paper.
Van Ceulen became so attached to the work that his contemporaries said he wore himself out and died from it. That a person would exhaust himself this much just to find the digits of a number might look strange today. But in that era, approaching the exact value of pi was both a mathematical achievement and a kind of personal obsession. For van Ceulen, those 35 digits were the worth of a lifetime.
After his death, the digits were carved into his tombstone. In Germany, pi was long known by his name and called the "Ludolphine number." That a mathematician's tombstone carried the digits of a number rather than a formula remained a plain mark of how fully he had given himself to the work.
02
Not Pi, But an Incredible Simulation
Fraction 355/113
It is impossible to write the exact value of pi as a fraction, because pi is an irrational number. Even so, mathematicians have long searched for simple fractions that sit as close to pi as possible. The most surprising of these is 355/113. Worked out, it yields 3.1415929, and it sits so near pi's true value that the gap between them is smaller than one in a million. For this reason 355/113 is sometimes called "not pi, but an incredible simulation."
What makes this closeness so remarkable is how plain the fraction is. It uses only the digits 1, 3, and 5, each appearing twice. It is easy to remember and short to write, and yet it gives pi correctly to seven digits. Getting an approximation this good out of such small numbers is a rare thing in the world of fractions.
The fraction traces far back, to the fifth-century Chinese mathematician Zu Chongzhi. When Zu expressed pi with it, Europe would need roughly a thousand years to reach the same accuracy. Because it carries both simplicity and precision at once, 355/113 is still remembered today as the most elegant fractional approximation of pi.
03
Pi's Two Days on the Calendar
Dates 3/14 & 22/7
Pi has two separate days of celebration each year. The first is March 14, written "3/14" in the American style. Because this date lines up exactly with pi's first three digits, 3.14, it is known as Pi Day. In many parts of the world math lovers mark it with activities built around the circle, contests to recite pi's digits, and pies and tarts whose name echoes the number itself.
The second day is July 22, or "22/7." This date comes from 22/7, a fractional approximation of pi used since ancient times. Twenty-two divided by seven gives roughly 3.142, sitting even a touch closer to pi than 3.14 does. For this reason the day is called Pi Approximation Day. The difference between the two days is that one highlights pi's decimal form while the other highlights its expression as a fraction.
That a single number has separate days for both its decimal form and its fractional form shows how special a place pi holds in the human imagination. While most numbers find no place on any calendar, pi is one of the rare few celebrated twice a year.