Happy Pi Day

Jonathan writes "Today, the 14th of March, is Pi Day 2008. Pi Day is internationally celebrated in honor of the mathematical constant "Pi," who's actual value will — now and forever — remain unknown. NeoSmart Technologies has a run-down on the history of Pi, Pi Day, and the significance of Pi and other such "magical numbers" to science and technology. 'Pi isn't just a number that you can use to calculate circle-related mathematics, it's a symbol of something by far greater. Pi is one of many "magic" numbers that are found everywhere — if you know where to look. These magic numbers can't be explained, they just are. And if you use them right, they make it a lot easier to do a lot of really complicated things... In a way, they're a testimony to technology and computers (or vice-versa, depending on how you look at it).'"

Comments

Unknown value?

[ElizabethGreene]

I would not say that it has an unknown value, the value is known as the ratio of a circle's diameter and circumference. Just because our system of representing numbers is flawed in that it cannot accurately define numeric sequences that approach infinity doesn't mean it is unknown... That is like saying 1/3 is unknown just because you can't print enough 3's after the decimal place to be accurate.

Silly boys.

-ellie

Re:Unknown value?

[nine-times]

I'm sorry because I know I'm being pedantic, but I've dealt a fair amount with number theory and I felt like I should comment. You can't, strictly speaking, have "base pi" in the way that our number system is "base 10". If you don't quite know why that is the case, ask yourself if you wanted to count to "10" in "base pi" (which would be pi), what would that counting look like?

If you think it would be "1, 2, 3, 10" then you're talking about base 4. Otherwise, the distance on a number line between 0->1, 1->2, and 2->3 would all be equal to one unit, but 3->10 (the next number) would be 0.14159265... units.

The issue of pi being an irrational number, rather, is related to the definition of numbers as geometric ratios (which is how most of our mathematics consider numbers). The problem is that the diameter of a circle and the circumference are incommensurable, meaning that you can never come up with a whole-number ratio between those two lengths. Therefore, you cannot, no matter what length you choose as your unit, measure both the diameter and circumference with the same unit.

As a result, we generally take the diameter to be 1 unit of length, and the length of the circumference to be represented by the irrational number pi units of length. So the "number" of pi is an approximation of the ratio of diameter:circumference. We could just as easily assign the circumference to be the unit, however, and then the measurement usually represented by pi would be represented by "1" (which is what I think the GP post was alluding to). However, this would result in us having to deal with a different irrational number, which would be for representing the diameter, which would be 1/pi.

What do you mean by unknown?

[A beautiful mind]

who's actual value will -- now and forever -- remain unknown

Pi's value is known totally precisely, it is just that an irrational number cannot be represented using the good ol' rational numbers or any x/y form of them, it only can be approximated. That is why it is called an irrational number! It doesn't make pi any less definite though.

Re:What do you mean by unknown?

[Xcott Craver]

Pi's value is known totally precisely

Indeed, pi is exactly (ln -1)/(sqrt -1).

Re:What do you mean by unknown?

[CalvinTheBold]

Not exactly. I see what you are trying to do, though.

The problem with trying to write ln(e^(pi*i)) = ln(-1) is that the natural logarithm function defined over the complex numbers has a branch cut along the negative x-axis. Anywhere along that line, ln is not a single-valued function. One may alternately say that ln is holomorphic for all complex numbers whose imaginary part is nonzero, or whose imaginary part is zero and real part is positive.

This is why ln(x) is undefined for all x 0.

Re:Wrong day

[Neko-kun]

That's why my files get dated YYYY/MM/DD so as to avoid any unnecessary confusion. Makes it easier to sort too:D

Re:Wrong day

[Ed Avis]

YYYY-MM-DD would be better; the different delimiter character avoids confusion with other date formats. This is the standard date and time notation.

'course, if you're making subdirectories on a Unix filesystem, using / is handy.

These are the real pi moments

[Anonymous Coward]

For those of us on 64 bit surely:

date -d @3141592653
Sat Jul 20 20:37:33 EDT 2069

is the next pi moment.

You 32bit suckers have already passed the last one:

date -d @314159265
Sat Dec 15 21:27:45 EST 1979

And a long wait for the next pi moment after that:

date -d @31415926535
Sat Jul 13 02:15:35 EDT 2965

correction

[geekoid]

"pi is an approximation of the ratio of diameter:circumference"

PI is exactly the ratio of diameter:circumference, we can only express it as an approximation in our number system.

PI = (ln -1)/(sqrt-1)