Posts Tagged ‘Pi Day’

Happy Pi Day!

March 14, 2009

magnum_pi_cast

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Things that equal Pi

March 13, 2009

piSo 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:

brainfreeze_piday2009

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.)

dino-pi.png