Posts Tagged ‘Pi Day’

March 14, 2009

Things that equal Pi

March 13, 2009

So you want to make a pie for Pi Day, but you don’t want to decorate it with the traditional symbol $\pi$.  What other expressions could you use that are equivalent?

You could go with the elegant:  a picture of a circle and the ratio of the circumfirence to the diameter

$\frac{C}{d}$

In a similar vein, you could move up a dimension to area

$\frac{A}{r^2}$

or volume $\left(\frac{3V}{4r^3}\right)$, although in this case you’d have to draw a sphere and I can tell you right now that I’d lose points for clarity.

If geometry isn’t your thing, you could decorate your confection with an infinite sum, perhaps the Madhava-Gregory-Leibniz series (discovered by Madhava of Sangamagram, India about 600 years ago, and then rediscovered by James Gregory of Scotland and Gottfried Wilhelm Leibniz of Germany 200 years later)

$\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\cdots$

or the slightly more complicated

$\sqrt{\frac{6}{1}+\frac{6}{4}+\frac{6}{9}+\frac{6}{16}+\cdots}$

found by Leonard Euler of Switzerland in 1735.  Or even the Bailey-Borwein-Plouffe formula (which is, face it, kind of fun to say) that was discovered only 14 years ago(!) by Simon Plouffe of Quebec, Canada:

$\displaystyle\sum_{k=0}^{\infty}\frac{1}{16^k}\left(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6}\right)$

Incidentally, Simon Plouffe and Neil Sloane are the authors of the Encyclopedia of Integer Sequences, which gave rise to the online version.

But back to $\pi$.  Do you prefer products?  Then maybe you’d want to turn to Wallis’s product, discovered by John Wallis of England in 1655:

$2\cdot\left(\frac{2}{1}\cdot\frac{2}{3}\cdot\frac{4}{3}\cdot\frac{4}{5}\cdot\frac{6}{5}\cdot\frac{6}{7}\cdot\frac{8}{7}\cdot\frac{8}{9}\cdot\cdots\right)$

We’ll end on a more radical note:  the Viète formula, which was named after François Viète of France, but actually found by Euler.

$2\cdot\frac{2}{\sqrt{2}}\cdot\frac{2}{\sqrt{2+\sqrt{2}}}\cdot\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}\cdot\cdots$

Pi Day Sudoku 2009

March 9, 2009

Remember Pi Day Sudoku 2008?  Well the folk at Brainfreeze Puzzles have done it again!  Here’s their 2009 challenge:

Each row, column, and region contains the digits 1-9 exactly once plus three π symbols.  There’s a printable .pdf file here.

As a bonus, if you send a correct solution in to Brainfreeze puzzles in the next couple months, you’re eligible for a drawing for their book on Color Sudoku!  More details are on their website.

Happy Pi Day Week!

Edited 10/31 to add that the solution hasn’t been posted on the Brainfreeze site yet, but since it’s well past the contest deadline we approved a comment that has the solution (below).

Happy Pi Day!

March 14, 2008

From Dinosaur Comics last year. (Click for a legible version.)