## Happy Pi Day!

No, it’s not March 14.

But it is July 22, and that’s the day Girls’ Angle likes to celebrate Pi Day. Why? Because of Archimedes’ observation that the ratio of circumference to diameter in a circle is about 22/7.

In many ways, 22/7 is a more natural approximation for $\pi$ than 3.14. For one thing, it doesn’t depend on the choice of 10 as a base for a number representation system. For instance, in hexadecimal, $\pi = 3.243F\dots$. So much for March 14 in a hexadecimal society.

Besides, 22/7 is closer to $\pi$ than 3.14 is.  In fact, among all fractions p/q where p and q are positive and pq < 236, the fraction 22/7 is closest to $\pi$. (Which would cover all fractions obtained as a ratio composed from a month and a day as well as 3.14, which, as a fraction in lowest terms is 157/50. If you allow pq = 236, then we find the better approximation 179/57.) For more on rational approximations to $\pi$, read University of Michigan Associate Professor David Speyer’s two-part article starting in Volume 4, Number 2 of the Girls’ Angle Bulletin.

Still, the decimal digits of $\pi$ do seem to hold a special sway on the popular consciousness. So even though we prefer 22/7 to 3.14, here are the first several lines of a poem by Wislawa Szymborska (July 2, 1923 – February 1, 2012), the 1996 Nobel prize winner in literature:

Number Pi

three point one four one.
All the following digits are also initial,
five nine two because it never ends.
It can’t be grasped six five three five at a glance,
eight nine by calculation,
seven nine or imagination,
not even three two three eight by wit, that is, by comparison
four six to anything
two six four three in the world.
The longest snake on earth calls it quits after a few meters,
likewise, though a bit longer, snakes of myth and legend.
The pageant of digits comprising the number pi
does not stop at the edge of the page.
It goes on the table, through the air,
the wall, a leaf, a bird’s nest, clouds, straight into the sky,
through all heaven, endless and vast…

– Wislawa Szymborska

Special thanks to Konrad Malkowski of MathWorks for help with translating. The original Polish version may be found here, and a complete English translation by Stanislaw Baranczak and Clare Cavanagh may be found in Poems New and Collected by Wislawa Szymborska.

Would anyone care to write an Ode to 22/7?