Fun with Pi (Day)

We saw this picture on meeyauw, and thought it was a good way to open our own Pi Day offering. Pi Day, or π day is celebrated on March 14 (3/14) of every year.

π does turn up in some interesting places besides circles and standard trigonometry (and LOLcat photos). There is of course Euler's famous identity:

which unites π with four of the other most famous constants in mathematics: zero, 1, i (the imaginary root of -1) and e. But it also turns up in some more surprising places. Consider the well-known factorial function, where n! or “n factorial” is the product of all the integers between 1 and n. For example:

5! = 5×4×3×2×1 = 120.

Simple enough. But of course some troublemaker is eventually going to ask for the factorial of 1/2. Not so easy. Fortunately, there is a function, called the Gamma function, that provides a solution:

Not really as simple as the original integer-only factorial. Once calculus is involved, might as well forget about it. But if you go through the trouble of plugging in 1/2 to the formula, you get the following intriguing result:

or

So the factorial of one half is one half the square root of π. Who knew?

4 thoughts on “Fun with Pi (Day)”

  2. All I need to know about pi is that it is equal to r (radius) squared. Not to be confused with the fact that pi are not squre, they are round. 😉

    Happy Pi Day!!

    Sandi

  3. You asked: [i]Who knew?[/i]

    [b][i]WHO KNEW?[/i][/b]

    To quote [url=http://en.wikipedia.org/wiki/Pythagoras#Musical_theories_and_investigations]πythagoras[/url], teh awesome musical cat owned by [url=http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss]Gauss[/url] when he was a small boy of 3.14:

    [i]MAN, I SWEAR BY TEH TETRACHTYS OV TEH DECAD THAT EVRYBODY BUT THE IRRATIONAL EUCLID KNEW. AN NEVR FURRGET, CHEEZBURGER R ROUND! ILL EAT YOURS. DELISHUS.[/i]

    😛

    ps: I can't believe I missed Pi day. Maybe that's because I didn't know about it — and that saddens me. Next year at my house, though, a cheeseburgers and pie party, with all the retsina you can drink!

    Kronecker: [i]God created the integers; all else is the work of man.[/i]

    Happy weekend…

  4. Feh.

    [b]πythagoras[/b]

    In my previous comment, the symbol for pi was magically transformed into the above sequence of characters, along with the error, my bad, of an extraneous "y."

    So-o-o-o, I'm thinking, let's call the cat Pi-thagoras and pretend the [i]symbol[/i] for pi is there instead.

    KTHXBAI!

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