Tuesday, March 14, 2006

May Your Pi Day Be Irrational

Today is 3-14, or as it is known to many a Math major, Pi Day.

Pi Day dot Org describes Pi thusly:

Pi, a Greek letter, is the symbol for the ratio of the circumference of a circle to its diameter. It is approximately 22/7 and is usually calculated to 3 digits, 3.14. With the use of computers, Pi has been caculated to over 51 billion decimal places. Pi is an irrational number meaning it will continue infinitely without repeating. The symbol for pi, , was first used in 1737 by William Jones, but was popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737.

If you want to send that special someone a Pi Day card, do so here.

Math teacher Lavern Chirstionson wrote some Pi Day songs. Let's sing this one together:

Oh Number PI

Oh, number Pi
Oh, number Pi
Your digits are unending,
Oh, number Pi
Oh, number Pi
No pattern are you sending.

You're three point one four one five nine,
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.

Oh, number Pi
Oh, number Pi
You are a number very sweet,
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There's 2 Pi r and Pi r squared,
A half a circle and you're there,
Oh, number Pi
Oh, number Pi
We know that Pi's a tasty treat.

Pi is without a doubt the most interesting of numbers. Its history is complex, its exact determination impossible.

If you were thinking, "yeah" I would like to know about Pi Day and the types of activities that I could do at home with my kids who are flunking Algebra, here are some links:

A Pi Day reference page from Math teachers in St. Louis.

Exploratorium celebrates Pi Day, and points out that it is also Albert Einstein's birthday.



A great gift is the Pi Necklace.

Other Pi Day gifts.

The official Pi Day Org has lots of links, including Pi to one million digits.

I, thanks to scientific calculators that kept me entertained during boring math classes, memorized Pi to 15 digits in high school.

What is your favorite story about Pi? Did Pi help you calculate the amount of aluminum you needed to make a soda can with a 3 inch radius? Did it help you figure out how much rubber you needed to make a new tire for your SUV?

Have a fovorite Pi joke? "How do you reason with Pi?" A: You can't. It's irrational.

Please share on this great day.

38 Comments:

At 4:56 PM, Anonymous Homer said...

mmmmmm.... pi

 
At 7:07 PM, Blogger Cassandra said...

Yeah. Today's another holiday too, but I wasn't about to post about it.

 
At 7:09 PM, Blogger Cassandra said...

Here: an annoying PI link :)

 
At 7:28 PM, Blogger Josh Cummings said...

Happy Pi Day! Here is an interesting article on How To Celebrate Pi Day. Also, here are some nifty pi t-shirts for celebrating Pi Day.

 
At 9:31 AM, Blogger camojack said...

Holy crap, Cass...that IS freakin' annoying!!!

 
At 11:30 AM, Blogger Cassandra said...

I know it :D

The thing is, y'all love me anyway.

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At 5:48 PM, Anonymous Anonymous said...

Hi,

My name is Jason D. Padgett. I'm a physics/mathematics student in Washington state and I think I have found the solution to Pi.

I've always been taught that Pi sequence of numbers goes to infinity and never repeats. But that is at least partially incorrect.

They say that Pi goes to infinity because as you inscribe more and more polygons (or squares) within a circle you always have some space left over as you approach a circle (Pi being a limit as x approaches infinity). This is correct MATHEMATICALLY, but is incorrect when you look at the physical limits of measurement in the universe.

Pi ends when each side to a circle is one Planck length.

One equation that you can use to test this is, f(x)=xsin(pi/x)
In this equation as x approaches infinity f(x) approaches Pi. But again, Pi ends (physically) when each side to a circle equals one Planck length.

In integral form (I have to write it because the computer I'm on does not do equations:), would be,

the integral from -1 to 1 of the square root of 1-x^2 with n=planck length.

Since there are no measurements (that are relative to us) that are smaller than a Planck length the the limit that we can divide the integrals into is the Planck length.

So Pi ends in this situation also. Mathematically it will go forever, but the physics of Pi is what the universe actually uses.

Thanks and have a great day. I love your website. Any comments or questions just send me an email and mention that is about Pi so I don't erase it.

Sincerely,

Jason D. Padgett
JASONQUANTUM1@YAHOO.COM

 
At 10:21 PM, Anonymous Anonymous said...

Holy crap, I just graphed your Pi equation and it does exactly what you said. Not only that but it is the harmonic series. When you graph f(x)= xsin(Pi/x) the graph crosses the x axis at 1/1, 1/2, 1/3, 1/4....1/n. I also calculated what you were describing in integral form and you're correct. Pi would physically have an end (a relativistic, observational end)when the sub-intervals of the integral are the width of the Planck length. That's just cool!

Jeff

 
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