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dimanche 14 mars 2010

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THANK GOODNESS IT'S PI DAY! CELEBRATE WITH IRRATIONAL EXUBERANCE

March 10, 2010
http://www.xomba.com/thank_goodness_its_pi_day_celebrate_irrational_exuberance

March 14th is Pi Day, and that's official!

This tradition was started at the Exploratorium, in San Francisco, and 2010 will be their 22nd year of irrational exuberance. It also coincides with Einstein's date of birth – which was on 14 March 1879 – so it's a double celebration for geeks around the world.

But hold on, why March 14th? Well, the people at the Exploratorium obviously figured out that written out as numbers this date becomes 3-14, which are the first three digits in the decimal expansion of pi (3.14...) However, they are lucky to be Americans because this makes no sense whatsoever to most of the rest of humanity! In America, they like to write their dates as month-day-year whereas most of the planet use the seemingly more rational little endian form day-month-year. So irrationality really does triumph on Pi Day!

One other thing: what's with all the irrational puns? Glad you asked, pi is probably the most famous irrational number. Everyone has heard of it and seen it in their schoolbooks even if they haven't the foggiest what it means or where it comes from. In the mathematical use of the word, “irrational” does not mean that psychiatric help is needed but rather that the number cannot be expressed as a “ratio” or fraction. Thus we have rational numbers (such as 3/4 or 22/7) and we have irrational numbers (such as pi and root-2). Furthermore, numbers such as root-2 are known as algebraic because they are solutions of algebraic equations, in this case the rather simple x^2-2=0. However, there are no algebraic equations over whole numbers, however complicated, that bring forth the answer pi. For this reason, pi is also known as a “transcendental” number. But jokes about transcendental irrationality are few and far between and would probably be treading on theological ground.

Before calculators (and even before decimal notation) various cultured employed approximate values of pi to make their calculations easier. For example, 22/7 (3.1428...) was used by the Egyptians whereas 25/8 (3.125) has been found in Babylonian texts. These are, however, practical approximations and not definitions of the number pi. You can calculate your own value by taking any round object, such as a cylindrical jar. Take some sewing thread or thin string and wrap it around the circumference or perimeter of the object – cut it so you have a measure of this circumference. Then stretch the thread across the diameter of the circle, making sure to cross the centre – again cut this to the length of the diameter. Now, with a ruler, measure the two lengths of string. Divide the larger number by the smaller number and there you have it – your experimental value of pi.

OK, but why is it called pi anyway? How can a letter be a number? As we've just seen, the simplest geometric definition of pi is the ratio of the circumference of a circle to its diameter. A circumference is a fancy word for perimeter and the Greek word for perimeter starts with the letter pi. This was made popular in the early18th century and has stuck. As the number itself is infinitely long and tedious to write down (even if only to a few digits) it is simpler to just have a special symbol to represent it until such time as we need to perform a calculation. Pi is not unique in this respect as there are other numbers represented by letters, such as, the base of natural logarithms “e” and the Golden Ratio “phi”.

So, what fun things can you do on Pi Day? This year it falls on a Sunday so there's the whole day to enjoy. The Exploratorium has posted a schedule of events, so if you live in San Francisco then make a day of it. For those not so lucky, there is a webcast plus live events at the Exploratorium on Second Life. It seems to involve eating a lot of pie too (I know, feeble pun) so best to buy your own as eating virtual pie isn't much fun at all.

The Pi Day website also has a page of links to interesting resources such as videos, games, activities and even Pi Day greeting cards. However, one thing they've missed is “Pi” the movie. This is an intense psychological thriller in which mathematician Max Cohen is hounded for a “secret number” spewed out by his erratic computer. One group wants to use it to predict the stock market, the other believe it reveals the name of God. This bivalence of mathematics goes all the way back to Pythagoras's influence on Plato, who wrote that mathematics is unique in that it is both the handmaiden of science and the key to mystical wisdom. Looks like we've come round to irrational transcendentalism again!

What are the best internet resources about pi? One interesting website is the Pi-Search Page. Here you can input any number you wish and find out if that number exists within the decimal expansion of pi. This search engine uses the first 200 million digits of pi so you should be able to find your birthday lurking in there somewhere. The statistics of this are also quite interesting in that there is a 99.995% chance of finding a 7-digit number, but this drops to 63% for an 8-digit number (like a birthday) and stumbles precipitously to just 9.5% for a 9-digit search. Is this normal behaviour for a number or not?

However, the record for the number of digits of pi now stands at 2.7 trillion. And this was done with a mere home computer, albeit turbo-charged. Trying to memorize so many digits seems to be a Herculean task. The record for the most number of digits of pi to be successfully remembered is an astonishing 67,890 by Chau Lu, from China. How many can you recite? The easiest way to remember such random digits is to use a mnemonic. There are many such memory aids for pi, but the one that made me smile most is,”How I wish I could calculate pi.” So simple and yet by counting the number of letters in each word we get the expansion 3.141592, which is more than adequate enough for most purposes.

If memorizing random numbers seems a tough call then remembering facts should be easier. The Pi Trivia Game is a bit tough on the old memory but has lots of nuggets of information... once you look at the answers! If you find any other really useful (or even slightly bizarre!) websites about pi then let everyone know by adding a comment below.

Happy Pi Day